Question

From a solid cylinder whose height is 2.4 cm and the diameter 1.4 cm, a cone of the same height and same diameter is carved out. Find the volume of the remaining solid to the nearest cm³.

Answer 1

Radius of a cylinder = Radius of a cone (r) = 0.7 cm

Height of a cylinder = Height of a cone (h) = 2.4 cm

Volume of the remaining solid = Volume of the cylinder – Volume of a cone

= `pi"r"^2"h" - 1/3 pi"r"^2"h"  "cm"^3`

= `pi"r"^2"h" (1 - 1/3) "cm"^3`

= `22/7 xx 0.7 xx 0.7 xx 2.4 xx 2/3 "cm"^3`

= `22/7 xx 7/10 xx 7/10 xx 24/10 xx 2/3 "cm"^3`

= `(22 xx 7 xx 24 xx 2)/(1000 xx 3) "cm"^3`

= `(22 xx 7 xx 8 xx 2)/(1000) "cm"^3`

= 2.464 cm³

= 2.46 cm³

Volume of the remaining soild = 2.46 cm³