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16. Surface Areas and Volumes
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Q7 of 107 Page 17

If the radii of the circular ends of a conical bucket 45 cm high are 5 cm and 15 cm respectively, find the surface area of the bucket.

Given: for the bucket,


Height = 45cm


r’ = 5cm


r’’ = 15cm


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


= π(5 + 15)(26) + π (15)2


= 745 π cm2


Curved surface area of bucket = 745π cm2


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5

If the radii of the circular ends of a conical bucket which is 45 cm high be 28 cm and 7 cm, find the capacity of the bucket.

6

The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

8

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

9

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m, the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent.

Questions · 107
16. Surface Areas and Volumes
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