Q30 of 32 Page 13

The volume of two hemispheres are in the ratio 8 : 27. Find the ratio of their radii.

Let the volumes of two hemispheres be V1 and V2 and the radii be r1 and r2 respectively.
Therefore the required ratio of their radii=
Hence, the ratio of the radii, r1 : r2 = 2 : 3

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28 The surface area of a sphere and the curved surface area of a cylinder are in the ratio 2 : 1. Find the ratio of their volumes, if their radii are equal. 29 Find the volume of the greatest sphere that can be cut of a cube of side 14 cm. Find also the volume of the remaining piece. 31 A small indoor greenhouse (herbarium) is made entirely of glass panes (Including base) held together with tape. It is 30cm long, 25cm wide and 25 cm high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges? 32  A Joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.