Question

If the volume of cone is 12 m and height is 4 m. Then find its diameter

Answer 1

v = 12 m

h = 4m

Solution:

$v = \pi {r}^{2} \times \dfrac{h}{3} \\ \\ \to{}v = \frac{22}{7} \times {r}^{2} \times \frac{4}{3} \\ \\ \to{}v = \frac{88}{21} \times {r}^{2} \\ \\ \to{} r²= \frac{12 \times 21}{88} \\ \\ \to{} r² = \frac{252}{88} \\ \\ \to{}r² = 2.9$

r = 1.7

.°. d = 3.4 m

so done ^^

Answer 2

Step-by-step explanation:

Given:-

the volume of cone is 12 m^3 and height is 4 m.

To find:-

If the volume of cone is 12 m^3 and height is 4 m. Then find its diameter

Solution:-

Height of the cone (h)=4 m

Let the Radius of the cone be "r" m

Volume of a cone = (1/3)πr^2h cubic units

=>V = (1/3)×(22/7)×r^2×4 cubic m

=>(1×22×4×r^2)/(7×3) cubic m

=>V= 88r^2 / 21 cubic m

According to the given problem

Volume of the cone is 12 m^3

=>88r^2/21 = 12

=>88r^2 = 12×21

=>88r^2 = 252

=>r^2 = 252/88

=>r^2 = 63/22

=>r= √(63/22)

=>r = √(9×7/22)

=>r = 3√(7/22)

Radius of the given cone = 3√(7/22) m

Diameter = 2×radius

Diameter of the given cone = 2×3×√(7/22) m

=>D = 6√(7/22) m

(or)

on multiplying both numerator and denominator by 22 then

=> D = 6√[(7/22)×(22/22)

=>D = 6√[(7×22)/(22×22)]

=>D = 6√154/22

=>D = (3/11)√154

=>D = (3√154)/11 m

(or)

=>D = 3×12.4/11 m

=>D =37.2/11 m

=>D = 3.38 m (approximately)

=>D = 3.4 m (Correct it one place)

Answer:-

Diameter of the given cone = (3√154)/11 m

(or) 3.38 m (or) 3.4 m

Used formulae:-

• Volume of a cone = (1/3)πr^2h cubic units
• Diameter = 2×radius