Question

The ratio of the base radius and the height of cone is 3 : 4. If the cost of smoothening the curved surface area at 5 paise/sq cm is 115.30, then the volume of the cone is

Answer 1

Step-by-step explanation:

CSA = 11530÷5 = 2306CM²

πrl =2306cm²

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

$\frac{22}{7} \times r \times \sqrt{ {r}^{2} + {h}^{2} } = 2306$

let the common ratio between r&h =x

r= 3x

h=4x

$\frac{22}{7} \times 3x \times \sqrt{ {(3x)}^{2} + {(4x)}^{2} } = 2306$

66x/7 × √{9x²+16x²} = 2306

66x/7 ×5x = 2306

330x²/7 =2306

x² =2306×7/330

x²= 49(approx.)

x=7

r=3×7=21cm

h=4×7=28cm

$volume \: of \: cone \: = \: \frac{1}{3} \pi {r}^{2} h$

=1/3 ×22/7 ×21²×28

=12936cm³