Question

A hemispherical bowl is made up of stones whose thickness is 7 cm. If the inner radius is 35 cm, find the total surface area of the bowl.

• A. $20463.38c{m}^2$
• B. $18942c{m}^2$
• C. $15942c{m}^2$
• D. $18992c{m}^2$

Answer 1

The correct option is A $20463.38c{m}^2$

We know that,
Curved surface area of hemisphere
$=2\pi r^2$

Now,
Total surface area
= Inner curved surface area + Outer curved surface area + Area of thickness

Now,
Inner radius of hemisphere ($r_i$)
= 35 cm
Outer radius of hemisphere ($r_o$)
= 35 cm + 7 cm
= 42 cm

Inner curved surface area
$=2\pi r^2$
$=2\times \pi \times {35}^2$
$=7693c{m}^2$

Outer curved surface area
$=2\pi r^2$
$=2\times \pi \times {42}^2$
$=11077.92c{m}^2$

Area of thickness
$=\pi \left(\right(r_o{)}^2-\left(r_i{)}^2\right)$
$=\pi ({42}^2-{35}^2)$
$=1692.46c{m}^2$

$\therefore$ Total surface area
$=7693+11077.92+1692.46$
$=20463.38c{m}^2$