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

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

Options
a) 704 cm²
b) 806 cm²
c) 904 cm²
d) 608 cm²

Solution

As per question
Volume of cone = $\frac{1}{3} \times \pi \times r^2 \times h$
Total curved surface area = πrl+πr²
l²= r² + h²
r = radius
h = height
l = slant height
Volume of cone = $\frac{1}{3} \times \pi \times r^2 \times h$
1232 = $\frac{1}{3} \times \frac{22}{7} \times r^2 \times 24$
$r^2 = \frac{1232 \times 3 \times 7}{22 \times 24}$
r² = 49
r = 7
l²= r² + h²
l²= 7² + 24²
l²= 49 + 576
l² = 625
l = $\sqrt{625}$
l = 25

Total curved surface area = πrl+πr²
Total curved surface area = $\frac{22}{7} \times 7 \times 25 + \frac{22}{7} \times 7 \times 7$
Total curved surface area = 22 x 25 + 22 x 7
Total curved surface area = 550 + 154 = 704 cm²

Answer: a) 704 cm²