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Important Questions

Surface Areas and Volumes

Editorially selected priority revision questions for this chapter.

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Important Questions

5

Q1

Hard Concept

A toy is in the form of a cone of radius $3.5$ cm mounted on a hemisphere of the same radius. The total height of the toy is $15.5$ cm. Find the total surface area of the toy. (Take $\pi = \frac{22}{7}$ )

Q3

Long Answer (5 Marks)

A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is $26$ cm, while the height of the conical part is $6$ cm. The base of the conical portion has a diameter of $5$ cm, while the base diameter of the cylindrical portion is $3$ cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $\pi = 3.14$ )

Q4

Long Answer (5 Marks)

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $2$ cm and the diameter of the base is $4$ cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take $\pi = 3.14$ )

Q5

Long Answer (5 Marks)

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.

Q7

Long Answer (5 Marks)

A metallic bucket, open at the top, is in the shape of a frustum of a cone. The height of the bucket is $24$ cm, the radius of the upper circular end is $14$ cm, and the radius of the lower circular end is $7$ cm. Find: (i) the area of the metallic sheet used to make the bucket (ignoring the thickness of the metal), and (ii) the volume of water the bucket can hold. (Take $\pi = \frac{22}{7}$ )

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