Question

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. The surface area of the toy is _____ (Use $\pi =3.14$)

• A. $47.1c{m}^2$
• B. $56.52c{m}^2$
• C. $103.62c{m}^2$
• D. $160.14c{m}^2$

Answer 1

The correct option is C $103.62c{m}^2$

Given that, a toy is in the form of a cone surmounted on the hemisphere. Diameter of the base d = 6 cm and the height of the cone h = 4 cm, then we have to find the surface area of the toy.

The radius of the base is
$r=\frac{d}{2}=\frac{6}{2}=3cm$

The slant height of the cone is
$l=\sqrt{r^2+h^2}=\sqrt{3^2+4^2}=5cm$

We know that,
Surface area of cone
$=r\pi l$
$=3.14\times 3\times 5$
$=47.1c{m}^2$

Surface area of hemisphere
$=2\pi r^2$
$=2\times 3.14\times 3^2$
$=56.52c{m}^2$

Therefore, surface area of the toy
= surface area of cone + surface area of hemisphere
$=47.1+56.52$
$=103.62c{m}^2$