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Mathematics : Surface Areas and Volumes

Short Answer Type

621. A sector of a circle of radius 15 cm has the angle 120°. It is rolled up so that two bounding radii are joined together to form a cone. Find the volume of the cone

open parentheses straight pi equals 22 over 7 close parentheses

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622. A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the major and minor segments. (Take

straight pi

= 3.14).

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623. The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

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624. The inner circumference of a circular track is 440 m and the track is 14m wide. Calculate the cost of levelling the track at the rate of 25 paise per sq. m. Also find the cost of fencing the outer circle at the rate of Rs. 5 per m.

left parenthesis space U s e space straight pi space equals space 22 over 7 right parenthesis

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625. A rectangle 8 cm x 6 cm is inscribed in a circle as shown in figure. Find the area of the shaded region (use

straight pi

= 3.14).

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626. A chord AB of a circle of radius 14 cm makes a right angle at the centre (O) of the circle. Find the area of the miner segment (Take π =

22 over 7

)

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627. A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm, 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.

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628. A hemisherical bowl of internal radius 9 cm, is full of water. This water is to be filled in cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of bottles needed to fill the whole water of the bowl. (use π =

22 over 7

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629. A conical vessel whose internal radius is 5 cm and height 24 cm is full of water The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height to which the water rises in the cylindrical vessel.

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630. The internal and external radii of a hollow sphere are 3 cm and 5 cm respectively. The sphere is melted to form a solid cylinder of height 22/3 cm. Find the diameter and curved surface area of the cylinder.

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