A solid metallic sphere of radius 6 c m is melted and made into a solid cylinder of height 32 c m . Find the curved surface area of the cylinder. (Take π = 3 . 1 )

Radius of metallic sphere R = 6 c m Height of cylinder h = 32 c m Volume of cylinder = Volume of metallic sphere π r 2 h = 4 3 π R 3 r 2 × 32 = 4 3 × 6 3 r 2 = 4 × 6 × 6 × 6 3 × 32 r 2 = 9 r = 3 c m Then, curved surface area of the cylinder = 2 π r h = 2 × 3 . 1 × 3 × 32 = 595 . 2 c m 2

A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows: The height of the solid cylinder is 7 c m , radius of each of hemisphere, cone and cylinder is 3 c m . Height of cone is 3 c m . Give your answer correct to nearest whole number. Take π = 22 7 .

Radius of each of hemisphere, cone and cylinder is = 3 c m Height of cylinder = 7 c m Height of cone = 3 c m Now, Volume of cone = 1 3 πr 2 h = 1 3 × π × 3 2 × 3 = 9 π cm 3 Volume of Hemisphere = 2 3 πr 3 = 2 3 × π × 3 3 = 18 π cm 3 Volume of cylinder = π r 2 h = π × 3 2 × 7 = 63 π Required volume = Volume of cylinder - volume of hemisphere - volume of cone = 63 π - 18 π - 9 π = 36 π = 36 × 22 7 = 113 . 114 = 113 Therefore, volume of the remaining solid to nearest whole number is 113 c m 3