Math Is Fun Forum

Jai Ganesh

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Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 361. A right circular solid cylinder of base radius 4 centimeters and vertical height 22.5 centimeters is melted to form 8 equal solid spheres. If there is a process loss of 20% during such formation, then that is the radius of each of the solid spheres so formed?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 362. 2 centimeters of rain has fallen on a square kilometer land. Assuming 50% of the raindrops could have been collected and contained in a pool having a 100 meter x 10 meter base, by what level would the water level in the pool have increased?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 363. 4 pipes each of 3 inch diameter are to be replaced by a single pipe discharging the same quantity of water. What should be the diameter of the single pipe, if the speed of water is the same?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 364. A cone, a hemisphere, and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. Find the ratio of their total surface areas.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

.

M # 365. The cost of paint is $36.50 per kilogram. If 1 kilogram of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 366. If the lateral surface of a right circular cone is 2 times its base, then find the semi-vertical angle of the cone.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 367. There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 368. If the height of a cone is half the radius of a sphere then the radius of the base of the cone, which has the same volume as a sphere of radius 7 centimeters is _______ centimeters.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 369. Find the volume of a pyramid of base area 25 square centimeters and height 12 centimeters.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 370. If a rectangular paper of length 6 centimeters and width 3 centimeters is rolled to form a cylinder with height equal to the width of the paper, then find its radius.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

.

M # 371. A trapezium based prism is with two parallel sides 8 centimeters and 14 centimeters respectively and distance between two parallel sides is 8 centimeters. Find the height of the prism if the volume of the prism is 1056 cubic centimeters.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 372. A rectangular block has length 10 centimeters, breadth 8 centimeters, and height 2 centimeters. From this block, a cubical hole of side 2 centimeters is drilled out. Find the volume and the surface area of the remaining solid.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 373. A hollow garden roller 42 centimeters wide with a girth of 132 centimeters is made of iron 3 centimeters thick. Find the volume of the iron of the roller.
Use

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

.

M # 374. Three cubes are placed  adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the total surface areas of the cubes.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Mensuration

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

The solution

is correct. Excellent, Monox D. I-Fly!

M # 375. If the base of a rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be reduced by
(a) 50%
(b) 33.33%
(c) 66.66%
(d) None of these.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 376. Find the length of the longest rod that can be placed in a room which is 12 meters long, 9 meters broad, and 8 meters high.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 377. A hollow spherical shell is made of metal of density 4800 kilograms per meter cube. If its internal and external radii 10 centimeters and 12 centimeters respectively, find the weight of the shell in kilograms. Use

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 378. A right circular cone and a hemisphere have equal base diameter and equal volumes. Find the ratio of their heights.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 379. A conical cavity is drilled in a circular cylinder of height 15 centimeters and 16 centimeters base diameter. The height and the base diameter of the cone are same as those of the cylinder. Determine the total surface area of the remaining solid. (Give the answer in terms of

).

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 380. If the radius of a sphere is increased by 2 centimeters, then its surface area increases by 352 square centimeters. Find the radius of the sphere before the increase. Use

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 381. Find the lateral surface area of a regular pyramid with triangular base, if each edge of the base measures 8 centimeters and slant height is 5 centimeters.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 382. Find the total surface area of a pyramid with a square base if each side of the base measures 16 centimeters, the slant height of a side is 17 centimeters, and the altitude is 15 centimeters.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 383. The Perimeter of a semicircular path is 36 meters. Find the area of this semicircular path. Use

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,413

Re: Mensuration

Hi,

M # 384. The radii of two circles are 10 centimeters and 24 centimeters. Find the radius of a circle whose area is the sum of the area of these circles.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.