Question

A bucket is in the form of a frustum of a cone, its depth is $15cm$ and the diameter of top and bottom are $56cm$ and $42cm$ respectively. Find how many litres of water can the bucket hold. [Take $\pi =22/7$]

Answer 1

Height$h=15$cm

Top diameter$2r_1=56$cm$\Rightarrow$ radius $r_1=\frac{56}{2}=28$cm

Bottom diameter$2r_2=42$cm$\Rightarrow$ radius $r_2=\frac{42}{2}=21$cm

Volume of the cone$=\frac{1}{3}\pi h\{{\left(r_1\right)}^2+{\left(r_2\right)}^2+r_1{r}_2\}$

$=\frac{1}{2}\times \frac{22}{7}\times 15\times \{784+441+588\}$

$=28490{cm}^3$

Since $1$litre$=1000{cm}^3$

Capacity of the bucket it can hold$=\frac{28490}{1000}$litres$=2.849$litres