My little sister's filling a conical bag with gems. She knows that the capacity of each bag is 75.36 cubic inches. Find the slant height of the cone, up to three decimal places if the diameter is 6 inches {Use pi = 3.14}?

Correct option is D

Given:

Volume of cone (V) = 75.36 cubic inches

Diameter of cone = 6 inches

π ≈ 3.14

Formula Used:

​$$r = \frac{\text{Diameter}}{2}$$​​

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

slant height $$s = \sqrt{r^2 + h^2}$$​​

Solution:

r = $$\frac{6 \text{inches }}{ 2}$$​ = 3 inches

75.36 =  $$\frac{1}{3}$$​$$\times$$​3.14 $$\times$$​ (3)² $$\times$$ h

75.36 = 3.14$$\times$$  3 $$\times$$ h
75.36 = 9.42h

h = $$\frac{75.36 }{ 9.42}$$​​

h = 8 inches

​$$s = \sqrt{r^2 + h^2}$$​​

s = $$\sqrt{(3² + 8²)}$$​​

s = $$\sqrt{(9 + 64)}$$​​

s = $$\sqrt{73}$$​​

s ≈ 8.544 inches (rounded to three decimal places)

Option (D) is right.