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16. Surface Areas and Volumes
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Q16 of 107 Page 17

A solid is in the shape of a frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the height id 9 cm. Find the area of its whole surface and the volume.

Given: height of the frustum = 9cm


Radius of its lower and upper ends: r’ = 30cm and r’’ = 18cm


Let slant height be l


Slant height, l =



⇒ l = 15cm


Volume =



= 5292 π cm3


Total surface area = π(r’ + r’’)l + π r’2 + π r’’2


= π(30 + 18)15 + π (30)2 + π (18)2


= 1944π cm2


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14

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.

15

A bucket made up of a metal sheet is in the form of 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 .

17

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is . The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs. 1.40 per .

18

A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by a plane parallel to its base. Find the ratio on the volumes of two parts of the cone.

Questions · 107
16. Surface Areas and Volumes
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