Question

A toy is in the form of a cone of radius $3.5$ cm mounted on a hemisphere of same radius. The total height of the is $15.5$ cm. Find the total surface area of the toy.

• A. $234.5c{m}^2$
• B. $224.5c{m}^2$
• C. $214.5c{m}^2$
• D. $204.5c{m}^2$

Answer 1

The correct option is C $214.5c{m}^2$

Given,

Radius of a cone is $3.5$cm,

Height of a cone is $15.5-3.5=12$cm

Slant height of cone is,

$l=\sqrt{h^2+r^2}$

$=\sqrt{{12}^2+{3.5}^2}$

$=\sqrt{144+12.25}$

$=\sqrt{156.25}$

$=12.5$cm

Curved surface area of cone is,

$=\pi rl$

$=\frac{22}{7}\times 3.5\times 12.5$

$=137.5c{m}^2$

Curved surface area of hemispherical portion is,

$=2\pi r^2$

$=2\times \frac{22}{7}\times 3.5\times 3.5$

$=77c{m}^2$

Hence,

total surface area,

$137.5+77=214.5c{m}^2$