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Surface Areas and Volumes

Short Answer Type

431.

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

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432. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

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433. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

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434.

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

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435.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.

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436.

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

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437.
A fez, the cap used by the Turks, is shaped like the frustum of a cone (see Fig. 13.24). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Let R and r be respectively the radii of bigger and smaller ends of the frustum and l be the slant height then.

R = 10 cm; r = 4 cm and l = 15
Now,
Curved Surface Area
= π Rl + πrl
= πl (R + r)

$equals space 22 over 7 straight x space 15 space left parenthesis 10 space plus 4 right parenthesis space cm squared equals space open parentheses 22 over 7 straight x space 15 space straight x space 14 close parentheses space cm squared equals space 22 space straight x space 30 space equals space 660 space cm squared$

and area of the top of the cap

$equals space πr squared equals space 22 over 7 straight x space 16 equals space 352 over 7 space cm squared$

Thus,
Total area of the material used for making the cap

$equals space open parentheses 660 plus 352 over 7 close parentheses space cm squared equals space 710 2 over 7 space cm squared$

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438.

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ` 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ` 8 per 100 cm2 . (Take π = 3.14)

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Long Answer Type

439.

A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter $1 over 16 cm$ , find the length of the wire.

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Short Answer Type

440.

A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm³.

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