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Mathematics : Surface Areas and Volumes

Short Answer Type

561. A tent is in the shape of a right circular cylinder up to a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs. 2 per sq. metre, if the radius of base is 14 m.

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562. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find total surface area.

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563. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

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564. Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere given in Fig. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour.

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565. A tent is in the shape of a cylinder up to a height of 5 m and then becomes a cone with a maximum height of 21 m above the ground. Calculate the cost of painting the inner side of the tent at Rs. 2 per m² if the radius of the base is 63 m.

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566. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the total surface area of the solid.

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567. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 108 cm and the diameter of the hemispherical ends is 36 cm, find the cost of polishing the surface of the solid at the rate of 7 paise per sq. cm.

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568. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rale of Rs. 100 per dm².

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569. A toy is in the form of a cone mounted on a hemisphere, with the same radius. The diameter of base of conical portion is 6 cm and its height is 4 cm. Find the surface area of the toy. (Use π = 3.14)

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570. A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is 18 cm and its height is 12 cm. Calculate the surface area of the toy.

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