Question

A toy is in the form of a cone mounted on a hemisphere of radius $3.5$ cm The total height of the toy is $15.5$ cm Then the total surface area is (Use $\pi =22/7$)

• A. $214.5$ $c{m}^2$
• B. $212.5$ $c{m}^2$
• C. $210.5$ $c{m}^2$
• D. $215.5$ $c{m}^2$

Answer 1

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

$\because$ Radius of the hemisphere =3.5 cm

$\therefore$ Radius of the base of the cone (r)=3.5 cm

Total height of the toy=15.5 cm

$\therefore$ Height of the conical part (h) =15.5-3.5=12 cm

$\therefore$ Slant height of the conical part (I)

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

$\sqrt{{12}^2+{\left(3.5\right)}^2}$

$\sqrt{144+12.25}$

$\sqrt{156.25}$

=12.5 cm

$\therefore$ Surface area of the conical part

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

$11\times 12.5=137.5c{m}^2$

Surface area of the hemispherical part

$2\pi r^2-2\times \frac{22}{7}\times {\left(3.5\right)}^2$

$22\times 3.5=77c{m}^2$

$\therefore$ Total surface area of the toy

=Surface area of the conical part + Surface area of the hemispherical part

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