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Mathematics : Surface Areas and Volumes

Short Answer Type

671. A gulab jamun, when ready for eating, contain sugar syrup of about 30% of its volume. Find approximately how much syrup would be found in 45 such gulab jamus, each shaped like a cylinder with two hemispherical ends, if the complete length of each of the m is 5cm and its diameter is 2.8 cm.

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672. A container shaped like a right circular cylinder having diameter 12 cm and diameter 6 cm, having a hemispherical shape and the top. Find the number of such cones which can be filled with ice-cream.

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673. A bucket made up of a metal sheet is in the formal a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket . Also find the cost of the bucket if the cost of metal sheet used is Rs. 20 per 100 cm². (Use

straight pi

= 3.14)

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674. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2m deep. If water flows through the pipe at the rate of 6 km/hr, in how much time will the tank be filled.

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675. A tent consists of frustum of a cone surmounted by a cone. If the diameters of the upper and lower circular ends of the frustrum be 14m and 26m respectively, the height of the frustum be 8m and the slant height of the surmounted conical portion be 12m, find the area of canvas required to make the tent. (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal)

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676. In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 14 cm, find the area of the shaded region.

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677. The length of a minor arc is

2 over 9

of the circumference of the circle. Write the measure of the angle subtended by the arc of the centre of the circle.

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678.

In the given Fig., the shape of the top of a table in a restaurant is that of a sector of a circle with centre O.

(i) the area of the top of the table. (ii) the perimeter of the table top.

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679. A spherical copper shell of external diameter 18 cm is melted and recast into a solid cone of base radius 14 cm and height

4 3 over 7

cm. Find the inner diameter of the shell.

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680. A bucket is in the form of a frustrum of a cone with cavity of 12308.8 cm³. The radii of the top and bottom circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of metal used in making it.

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