If the ratio of the height to the slant height of a cone is 4 : 5 and its volume is 12936 cm³, then what will be its diameter?
(Use value of π as 22/7)

Correct option is B

Given:
Volume of the cone = 12936 cm³
 Ratio of height to slant height = 4 : 5
Formula Used:
Pythagoras Theorem for Cone:
l² = h² + r²
Volume of Cone = (1/3) × π × r² × h
Solution:
Let height = 4x and slant height = 5x
Using Pythagoras Theorem:
(5x)² = (4x)² + r²
25x² = 16x² + r²
r² = 9x² => r = 3x
Volume = 12936
​$$\frac{1}{3} \times \frac{22}{7} \times (3x)^2 \times 4x = 12936 \\\frac{1}{3} \times \frac{22}{7} \times 9x^2 \times 4x = 12936 \\\frac{1}{3} \times \frac{22}{7} \times 36x^3 = 12936 \\x^3 = 343 \\x = 7 \\$$​​
Then radius = 3x = 21 cm
So diameter = 2 × 21 = 42 cm