Question

A toy is in the shape of a hemisphere surmounted by a cone. If the radius of the base of the cone is 3cm and height is 4cm, the total surface area of the toy is :

• A. $33\pi c{m}^2$
• B. $42\pi c{m}^2$
• C. $66\pi c{m}^2$
• D. $56\pi c{m}^2$
• E. $Noneofthese$

Answer 1

The correct option is A $33\pi c{m}^2$


Total surface area of toy
= Area of hemisphere + Area of cone
$=2\pi r^2+\pi rl$
$=2\times \pi \times \left(3^2\right)+\pi \times 3\times 5$
$=18\pi +15\pi =33\pi$
$(\therefore l=\sqrt{(3{)}^2+(4{)}^2}=\sqrt{25}=5)$