Question

A cone of height 24cm has a curved surface area 550cm square find its volume

Answer 1

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Answer 2

Given :

A cone of height 24cm has a curved surface area 550cm square

To Find :

find its volume

Solution:

Height of cone = 24 cm

Curved surface area of cone = $\pi r \sqrt{h^2+r^2} = \frac{22}{7} \times r \times \sqrt{r^2+24^2}$

We are given that curved surface area 550 cm square

$\frac{22}{7} \times r \times \sqrt{r^2+24^2}=550\\ r \times \sqrt{r^2+24^2}=550 \times \frac{7}{22}\\ r \times \sqrt{r^2+24^2}=175\\r=7$

Volume of cone = $\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times 24 =1232 cubic cm .$

Hence The volume of cone is 1232 cubic cm