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10th Assam Board
IMPORTANT
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Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminum sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Important Questions on Surface Areas and Volumes

MEDIUM
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 1
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 2
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 3
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
MEDIUM
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 5
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 6

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.2>Q 5
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.3>Q 4
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.
HARD
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.5>Q 7
Derive the formula for the volume of the frustum of a cone, using the symbols as explained.