Miscellaneous Mensuration (Simple)

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #131

There is some water in a cylindrical vessel of diameter 12 cm. A solid metallic sphere is fully immersed in to the water and the height of the water level in the vessel is increased by 1 cm. Calculate the diameter of the sphere.
Ans: 6 cm
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Question No: #132

A right-circular cylindrical drum has some water in it. 3 right-circular cone-shaped iron pieces of 32 cm base diameter and 40 cm height are completely immersed in the water so that the water level in the drum rises by 12.8 cm. Determine the diameter of the drum.
Ans: `40\sqrt{2}` cm
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Question No: #133

There are some water in a long gas jar of 7 cm diameter. If a solid right circular cylindrical pipe of iron having 5 cm length and 5.6 cm diameter be immersed completely in that water, calculate how much the level of water will rise.
Ans: 3.2 cm
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Question No: #134

There is some water in a right-circular cylindrical pot of diameter 24 cm. How much the height of water-level will be increased if 60 solid right-circular conical shaped iron pieces of diameter 6 cm and of height 4 cm each are completely immersed into that water ?
Ans: 5 cm
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Question No: #135

Half of a tank of length 21 dcm, breadth 11 dcm and depth 6 dcm is full of water. If 100 spheres made of iron and of diameter 21 cm each are fully immeresed into this water of tank, then how many dcm of the water-level of the tank will be raised ?
Ans: 2.1 dcm
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Question No: #136

The radius of a sphere and a right-circular cone are `r`. If their volumes are same, then height of the cone is -
(a) `r`, (b) `2r`, (c) `3r`, (d) `4r`
Ans: (d) `4r`
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Question No: #137

A solid sphere and a solid cone have the same radius. If the height of the cone is equal to the radius of the sphere, find the ratio of their volumes.

Question No: #138

Find the ratio of the volumes of a solid cone, a solid hemisphere and a solid cylinder when they have equal base diameter and equal height.

Question No: #139

Find the ratio of the volumes of a solid right circular cylinder, a solid right circular cone and a solid sphere when they have equal base diameter and equal height.
Ans: `3:1:4`
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Question No: #140

The surface area of a cube and a sphere are equal. Find the ratio of their volumes.
Ans: `\sqrt{11} : \sqrt{21}`
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