MEDIUM
10th Assam Board
IMPORTANT
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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.

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 4
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.useπ=227
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.
MEDIUM
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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MEDIUM
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 7
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ₹500 per m2. (Note that the base of the tent will not be covered with canvas.) 
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10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 8
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.
MEDIUM
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.1>Q 9

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

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MEDIUM
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.2>Q 1
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
HARD
10th Assam Board
IMPORTANT
MATHEMATICS Textbook for Class X>Chapter 13 - Surface Areas and Volumes>Exercise 13.2>Q 2
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.)