Question

Radii of the top and the base of a frustum are 12 cm, 6 cm respectively. Its height is 8 cm. Then,

• A. $2110.08c{m}^3$
  
• B. $1130.4c{m}^2$
• C. $565.2c{m}^2$

Answer 1

$r_1=12$ cm , $r_2=6$ cm, $h=8$ cm
Slant height of the frustum,
$l=\sqrt{h^2+(r_1-r_2{)}^2}$
$l=\sqrt{8^2+(12-6{)}^2}$
$l=\sqrt{64+36}$
$l=10$ cm
CSA of the frustum = $\pi (r_1+r_2)l$
= $3.14(12+6)10$
= $565.2c{m}^2$
TSA of the frustum = $\pi l(r_1+r_2)+\pi r_1^2+\pi r_2^2$
= $3.14\times 10(12+6)+(3.14\times {12}^2)+(3.14\times 6^2)$
= $1130.4c{m}^2$
Volume of the frustum = $\frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)$
= $\frac{1}{3}\times 3.14\times 8({12}^2+6^2+12\times 6)$
= $2110.08c{m}^3$​​​