Question

A milk carrying container has the shape of a cylinder mounted on a frustum. The radius of the cylinder is 14 cm and height is 20 cm. The other diameter of the frustum is 7 cm and its height is 5 cm. What is the curved surface area of the container?

• A. $1880c{m}^2\left(approx\right)$
• B. $201.12c{m}^2\left(approx\right)$
• C. $1060.5c{m}^2\left(approx\right)$
• D. $2399.65c{m}^2\left(approx\right)$

Answer 1

The correct option is D $2399.65c{m}^2\left(approx\right)$

Curved surface area of the required container = Surface area of cylinder + Surface area of frustum.

Radius of the cylinder, R = 14 cm
Height of the cylinder, h = 20 cm
Curved surface area of cylinder = $2\pi Rh$
= $2\times \frac{22}{7}\times 14\times 20$
= $1760c{m}^2$

Radii of the furstum are R and r, where R is 14 cm and r is 3,5 cm.
Slant height of frustum, l = $\sqrt{(14-3.5{)}^2+5^2}=11.63$

Curved surface area of the frustum = $\pi l(R+r)$
= $\frac{22}{7}\times 17.5\times 11.63=639.65c{m}^2$

$\therefore$ Total curved surface area of the container
= $1760c{m}^2+639.65c{m}^2=2399.65c{m}^2$