Question

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are $10cm$ and $30cm$ respectively. If its height is $24cm,$ find the area of the metal sheet used to make the bucket.

Answer 1

Diameter of lower end $\left(d_1\right)=10cm$

Radius of lower end $\left(r_1\right)=\frac{d_1}{2}=\frac{10}{2}=5cm$

Diameter of upper end $\left(d_2\right)=30cm$

Radius of upper end $\left(r_2\right)=\frac{d_2}{2}=\frac{30}{2}=15cm$

Height of bucket $=24cm$

Now,

$l^2={(r_2-r_1)}^2+h^2$

$\Rightarrow l^2={(15-5)}^2+{\left(24\right)}^2$

$\Rightarrow l=\sqrt{100+576}=26cm$

Now,

Area of metal sheet used in making bucket $=$ Curved surface area of bucket $+$ Area of base

Therefore,

Area of metal sheet used in making bucket $=\pi (r_1+r_2)l+\pi r^2$

$=3.14\times (15+5)\times 26+3.14\times 5^2=3.14\times 20\times 26+3.14\times 25=1632.8+78.5=1711.3{cm}^2$