Short Answer TypeHow 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?
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?
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.
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.
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. 
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)
Let R and r be respectively the radii of bigger and smaller ends of the frustum, then
R = 20 cm, r = 8 cm
Let l and h be respectively the slant height and height of the frustum then
h = 16 cm
Now,
(i) Curved Surface area of frustum
= πl (R + r)
= 3.14 x 20 (20 + 8)
= (3.14 x 20 x 28) cm2
= 1758.4 cm2
(ii) Total tin required
= CSA. + area of base
= 1758.4 + 3.14 x (8)2
= 1758.4 + 200.96
= 1959.36 cm2
(iii) Cost of required tin
(iv) Volume of frustum
Now,
Cost of the milk which can completely fill the container at the rate of 20 per litre
= 10.46 x 20
= Rs. 209.20
Hence, cost of milk is Rs. 209 and cost of metal is Rs. 156.75.
Long Answer TypeA 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 
, find the length of the wire.
Short Answer TypeA 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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