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Mathematics : Surface Areas and Volumes

Short Answer Type

631. A right triangle with sides 3 cm and 4 cm is revolved around its hypotenuse. Find the volume of the double cone thus generated.

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632. A solid metallic sphere of diameter 21 cm is melted and recasted into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed.

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633. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent, (use

straight pi

= 22/7).

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634. A solid metallic sphere of diameter 28 cm is melted and recasted into a number of smaller cones, each of diameter

4 2 over 3

cm and height 3 cm. Find the number of cones so formed.

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635. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.

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636. A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

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637. A hollow cone is cut by a plane parallel to the base and upper portion is removed. If the curved sarface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the altitude of the cone is divided by the plane.

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638. A toy is in the form of a cone mounted on a hemisphere of radius 3.5. cm. The total height of the toy is 15.5. Find the total surface area of the toy. (use

straight pi

= 22/7)

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639. If the radii of the circular ends of a bucket, 45cm high are 28 cm and 7 cm respectively. Find the capacity of the bucket.

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640. 50 circular plates, each of radius 7 cm, and thickness 1/2 cm, are placed one above the other to form a solid right circular cylinder. Find the total surface area and volume of the cylinder so formed, (use

straight pi

= 22/7)

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