Question

the perimeter of the ends of a frustum of a right circular cone is 44cm & 33cm.If the height of the frustum is 16cm,find is volume & total surface area.

Answer 1

see the attached file for solution. Thanks

Answer 2

Answer:

The volume and total surface area of frustum are  $1899.33 cm^3$ and $860.298 cm^2$ respectively.

Step-by-step explanation:

Circumference of one end of frustum = $2 \pi R$

So,$2 \pi R=44$

$2 \times \frac{22}{7} \times R = 44$

$R = \frac{44 \times 7 }{2 \times 22}$

$R = 7$

Circumference of other end of frustum = $2 \pi r$

So,$2 \pi r=33$

$2 \times \frac{22}{7} \times r= 33$

$r = \frac{33 \times 7 }{2 \times 22}$

$r = 5.25$

Height of frustum = 16 cm

Volume of frustum = $\frac{1}{3} \pi h (R^2+r^2+Rr)$

                               = $\frac{1}{3} \times \frac{22}{7} \times 16(7^2+5.25^2+7 \times 5.25)$

                               = $1899.33 cm^3$

Total surface area = $\pi (r+R)\sqrt{(R-r)^2+h^2}+\pi r^2 +\pi R^2$

= $\frac{22}{7} \times (5.25+7)\sqrt{(75.25)^2+16^2}+\frac{22}{7} \times 5.25^2 +\frac{22}{7} \times 7^2$

                              = $860.298 cm^2$

Hence the volume and total surface area of frustum are  $1899.33 cm^3$ and $860.298 cm^2$ respectively.