Question

from a solid cylinder whose height is 8cm and the radius is 6cm, a conical cavity of height 8cm and of base radius 6cm is hollowed out. find the volume of the remainning solid correct to two decimal places.Also find the surface area of the remaining solid.

Answer 1

$\bold{GIVEN,}$

◼For cylinder,

Height = 8cm

Radius = 6cm

$\boxed{Volume \: of \: cylinder = \pi {r}^{2} h}$

Volume of cylinder = $3.14 {6}^{2} 8$

$Volume\: of \:cylinder = 904.32 {cm}^{2}$

◼For cone,

Height = 8cm

Radius = 6cm

$\boxed{Volume \: of \: cone = \frac{1}{3} \times \pi \times {r}^{2} \times h}$

Volume of cone = $\frac{1}{3} \times 3.14 \times 6 \times 6 \times 8$

$Volume \: of \: cone =301.44 {cm}^{2}$

Volume of remaining solid= volume of cylinder - volume of cone

$Volume \: of \: remaining solid=608.88 {cm}^{2}$

Surface area of remaining solid = Surface Area of cylinder - surface area of cone

◼For cylinder

$\boxed{Surface \: area = 2\pi r h}$

Surface area = 2 × 3.14 × 6 ×8

Surface area = 301.44cm

◼For cone,

l = ?

b = 6cm

h= 8cm

By Pythagoras theorem,

${l}^{2} = {b}^{2} + {h}^{2}$

${l}^{2} = {6}^{2} + {8}^{2}$

${l}^{2} = 36 + 64$

${l}^{2} = 100$

$l = \sqrt{100}$

$l = 10 cm$

$\boxed{Surface \: area = \pi r l}$

Surface area = $3.14 × 6 × 10$

Surface area = 188.4cm

Surface area of remaining solid = Surface Area of cylinder - surface area of cone

Surface area of remaining solid = 301.44 - 188.4

Surface area of remaining solid = 113.04 cm