Question

If the radii of the circular ends of a bucket 28 cm high, are 28 cm and 7 cm, find its capacity and total surface area.

Answer 1

We have,

Height, h = 28 cm,

Radius of the upper end, R = 28 cm and

Radius of the lower end, r = 7 cm

Also,

The slant height, l = $\sqrt{(R-r{)}^2+h^2}$

= $\sqrt{(28-7{)}^2+{28}^2}$

= $\sqrt{{21}^2+{28}^2}$

= $\sqrt{441+784}$

= $\sqrt{1225}$

= 35 cm

Now,

Capacity of the bucket = $\frac{1}{3}\pi h(R^2+r^2+Rr)$

= $\frac{1}{3}\times \frac{22}{7}\times 28\times ({28}^2+7^2+28\times 7$

= $\frac{88}{3}\times (784+49+196)$

= $\frac{88}{3}\times 1029$

= 30184 cm3

Also,

Total surface area of the bucket = $\pi l(R+r)+\pi r^2$

= $\frac{22}{7}\times 35\times (28+7)+\frac{22}{7}\times 7\times 7$

= 110 x (35) + 154

= 4004 $c{m}^2$