Question

If the radii of the circular ends of a bucket $24$ cm high are $5$ cm and $15$ cm respectively, find the inner surface area of the bucket (i.e., the area of the metal sheet required to make the bucket)

(Take $\pi =3.14$)

• A. $1711.30c{m}^2$
• B. $1812.30c{m}^2$
• C. $1171.30c{m}^2$
• D. $1279.30c{m}^2$

Answer 1

The correct option is A $1711.30c{m}^2$

Material used to make the bucket $=$ Curved surface area $+$ Area of the base

Curved Surface area of a frustum of a cone $=\pi l(r_1+r_2)$ where $l$ is the slant height $=\sqrt{h^2+{(r_1-r_2)}^2}$ $h$ is the height.

$r_1$ and $r_2$ are the radii of the lower and upper ends of a frustum of a cone.

So, $l=\sqrt{{24}^2+{(15-5)}^2}$

$l=26\text{cm}$
Hence, Curved Surface area of this frustum of a cone $=3.14\times 26\times (15+5)=1632.8{\text{cm}}^2$
Area of the base $=\pi {r_1}^2=3.14\times 25=78.5\text{sq cm}$
So, the inner surface area of the bucket $=1632.8+78.5=1711.30{\text{cm}}^2$