Question

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 $c{m}^3$ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. $[Use\pi =\mathrm{3.14.}]$

Answer 1

We have,

Radius of the upper end, R = 20 cm and

Radius of the lower end, r = 12 cm

Let the height of the bucket be h.

As,

Volume of the bucket = 12308.8 cm3

⇒ $\frac{1}{3}\pi h(R^2+r^2+Rr)$ = 12308.8

⇒ $\frac{1}{3}\times 3.14\times h\times ({20}^2+{12}^2+20\times 12)$= 12308.8

⇒ 3.14$\frac{h}{3}\times (400+144+240)$=12308.8

⇒ $3.14\frac{h}{3}\times 784$=12308.8

⇒ h = $\frac{12308.8\times 3}{3.14\times 784}$

Therefore, h = 15 cm

So, the height of the bucket is 15 cm.