A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r
Question 1 Report
A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r
Answer Details
The volume of a sphere of radius r is given by the formula: \(\frac{4}{3}\pi r^3\).
The volume of a cylinder of radius 3cm and height 4cm is given by the formula: \(\pi (3cm)^2(4cm) = 36\pi cm^3\).
According to the question, the volume of the sphere is equal to the volume of the cylinder. Therefore:
\[\frac{4}{3}\pi r^3 = 36\pi\]
Dividing both sides by \(\frac{4}{3}\pi\), we get:
\[r^3 = 27\]
Taking the cube root of both sides, we get:
\[r = 3\]
Therefore, the value of r is 3cm. Answer is correct.
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