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Mathematics : Surface Areas and Volumes

Short Answer Type

681. The area of an equilateral triangle is

49 square root of 3

cm². Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles.

open square brackets Take space colon space square root of 3 equals 1.73 close square brackets

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682. In the given Fig. shows a decorative block which is made of two solids—a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere, fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.

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683. A juice seller serves his customers using a glass as shown in given Fig. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm. Find the apparent capacity of the glass and its actual capacity. [Use

straight pi

= 3.14]

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684.

A cylindrical vessel, with internal diameter 10 cm and height 10.5 cm, is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of
(i) Water displaced out of the cylinderical vessel,
(ii) Water left in the cylindrical vessel.

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