If a right circular cone of height 24 cm has a volume 1232 cm³, then the total surface area of the cone is (use π = 22/7).

Correct option is B

Given:

Volume of cone = 1232$$cm^{3}$$​​

Height of cone =24cm

Formula Used:

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

​$$Area \ of \ base = \pi r^{2}$$

Total surface area = Lateral surface area + Area of base​

​$$Total \ surface \ area = \pi r l + \pi r^{2}$$​​

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

Solution:

​$$Volume \ of \ cone=\frac{1}{3}\times\pi \times r^{2}\times h = 1232$$​

​$$\frac{1}{3}\times\frac{22}{7} \times r^{2}\times 24 = 1232$$​​

​$$r^{2} = \frac{1232\times 7\times 3}{22\times 24}$$​​

​$$r^{2}=49$$​​

r=7cm

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

l= $$\sqrt{7^{2}+24^{2}}$$​​

l=25cm

Lateral surface area of cone =$$\pi r l$$​​

=$$\frac{22}{7} \times 7 \times 25$$​​

= 550$$cm^{2}$$​​

Area of base =$$\pi r^{2}$$​​

= $$\frac{22}{7} \times 7^{2}$$​​

= 154$$cm^{2}$$​​

Total surface area = Lateral surface area + Area of base

= 550+154 = 704$$cm^{2}$$

Information Booster:

Using trigonometric triplets