The slant height of a cone is 5cm and its diameter is 8cm. What is the volume of the cone(correct to 2 decimal places )? (Where $$\pi = \frac{22}{7}$$)​

Correct option is B

Given:

Diameter of cone = 8cm

Slant height of cone =5cm

Formula Used:

Slant height =$$l= \sqrt{r^{2}+h^{2}}$$​​

Volume of cone=$$\frac{1}{3}\times\pi \times r^{2}\times h$$​​

Solution:

Radius of cone =$$\frac{8}{2} = 4cm$$​​

$$l= \sqrt{r^{2}+h^{2}} = 5$$​​

​$$4^{2}+h^{2} = 5^2$$​​

​$$h=\sqrt{25-16} = 3cm$$​​

Volume of cone$$=\frac{1}{3}\times\pi \times r^{2}\times h$$​​

​$$= \frac{1}{3}\times\frac{22}{7} \times 4^{2}\times 3$$​​

​$$= \frac{1}{3}\times\frac{22}{7} \times 4^{2}\times 3$$​​

​$$=\frac{22 \times 16}{7}$$​​

​$$= \frac{352}{7} =50.28cm^3$$​​