The volume of a cone of height 3cm is 38\(\frac{1}{2}\)cm3. Find the radius of its base. [Take \(\pi = \frac{22}{7}\)]
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Correct Answer: Option B
Explanation:
Using V = \(\frac{3}{1} \pi r^2h\),
so, 38\(\frac{1}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3\)
\(\frac{77}{2} = \frac{22}{7} \times r^2\)
r2 = \(\frac{77 \times 7}{2 \times 22}\)
r2 = \(\frac{49}{4}\)
Hence, r = \(\sqrt{\frac{49}{4}}\)
= 3\(\frac{1}{2}\)
Using V = \(\frac{3}{1} \pi r^2h\),
so, 38\(\frac{1}{2} = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 3\)
\(\frac{77}{2} = \frac{22}{7} \times r^2\)
r2 = \(\frac{77 \times 7}{2 \times 22}\)
r2 = \(\frac{49}{4}\)
Hence, r = \(\sqrt{\frac{49}{4}}\)
= 3\(\frac{1}{2}\)