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CBSE Class 9 Mathematics Question 27 of 44

Surface Areas and Volumes — Question 6

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Question

Question 4

If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.

Answer

Given,

Height of the cone (h) = 9 cm

Let radius of base of cone be r cm.

Volume of cone = 48π cm3

If the volume of a right circular cone of height 9 cm is 48π cm^3, find the diameter of its base. NCERT Class 9 Mathematics CBSE Solutions.

Substituting values we get :

⇒13πr2h=48π⇒r2=48π×3πh⇒r2=48×3h⇒r2=48×39⇒r2=1449⇒r2=16⇒r=16⇒r=4 cm.\Rightarrow \dfrac{1}{3}πr^2h = 48π \\[1em] \Rightarrow r^2 = \dfrac{48π \times 3}{πh} \\[1em] \Rightarrow r^2 = 48 \times \dfrac{3}{h} \\[1em] \Rightarrow r^2 = 48 \times \dfrac{3}{9} \\[1em] \Rightarrow r^2 = \dfrac{144}{9} \\[1em] \Rightarrow r^2 = 16 \\[1em] \Rightarrow r = \sqrt{16} \\[1em] \Rightarrow r = 4 \text{ cm}.

By formula,

Diameter = 2 × radius = 2 × 4 cm = 8 cm.

Hence, the diameter of base of cone is 8 cm.