Question

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 $cm$ with radii of its lower and upper ends as 8 $cm$ and 20 $cm$ respectively. Find the cost of the metal sheet used, if it costs ₹ 5 per 100 $c{m}^2$. (Take $\pi$ = 3·14)

• A. ₹ 92
• B. ₹ 95
• C. ₹ 98
• D. ₹ 100

Answer 1

The correct option is C

₹ 98

R = 20 cm, r = 8cm, h = 16 cm

slant height, $l$ =$\sqrt{h^2+(R-r{)}^2}$
= $\sqrt{256+144}cm$
= $20cm$

Surface area of the metal sheet used to make the container

= $\pi l(R+r)+\pi r^2=\pi \left\{l\right(R+r)+r^2\}$

= (3.14) $\times \{20\times 28+64\}c{m}^2$

= (3.14) $\times$ 624 $c{m}^2$

= 1959.36 $c{m}^2$

Therefore, the cost of the metal sheet at rate of ₹5 per 100 $c{m}^2$

= $₹1959.36\times \frac{5}{100}$
= ₹ 98 (approx.)