Question

The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm, and the other dimensions are as shown.

Find the total surface area of the solid.

Answer 1

Diameter = 10 cm

Therefore, radius (r) = 5 cm

Height of the cone (h) = 12 cm

Height of the cylinder = 12 cm

l = $\sqrt{h^2+r^2}$ = $\sqrt{{12}^2+5^2}$ = $\sqrt{144+25}$ = $\sqrt{169}$ = 13 cm

Total surface area of the solid:

= $\pi$rl + 2$\pi$rh + 2$\pi r^2$

= $\pi$(l + 2h + 2r)

= $\frac{22}{7}\times$5[13 + (2$\times$12) + 2$\times$5]

= $\frac{110}{7}$[13+24+10]

= $\frac{110}{7}\times 47$

= $\frac{5170}{7}$

= 738.57 $c{m}^2$