If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
Solution and Explanation
Height (h) of cone = 9 cm
Let the radius of the cone be r.
Volume of the cone = 48\(\pi\) cm³
\(\frac{1}{3}\pi\)r²h = 48π cm³
r² =\(\frac{ 48 \ cm^3 × 3 }{ h}\)
r² = \(\frac{48\ cm^3 × 3 }{ 9\ cm}\)
r² = 16 cm²
r = \(\sqrt{16}\) cm²
r = 4 cm
Diameter of base d = 2 × radius(r)
= 2 × 4 cm
= 8 cm
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