Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?
Option 1: 7 cm
Option 2: 10 cm
Option 3: 9 cm
Option 4: 8 cm

Question

Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?

Option 1: 7 cm

Option 2: 10 cm

Option 3: 9 cm

Option 4: 8 cm

Team Careers360 · Accepted Answer

Correct Answer: 8 cm

Solution : The volume of a sphere = $\frac{4}{3}\pi r_{ ext{s}}^3$
Where $r_{ ext{s}}$ is the radius of the sphere.
The volume of a cylinder = $\pi r_{ ext{c}}^2 h_{ ext{c}}$
Where $r_{ ext{c}}$ is the radius of the base of the cylinder and $h_{ ext{c}}$ is the height of the cylinder.
Given that the sphere and the cylinder have the same volume and the same radius.
$⇒\frac{4}{3}\pi r_{ ext{s}}^3 = \pi r_{ ext{c}}^2 h_{ ext{c}}$
Since $r_{ ext{s}} = r_{ ext{c}} = \frac{12}{2}$ = 6 cm
$⇒\frac{4}{3}\pi (6)^3 = \pi (6)^2 h_{ ext{c}}$
$⇒h_{ ext{c}} = \frac{4}{3} (6) = 8$
Hence, the correct answer is 8 cm.

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Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?Option 1: 7 cmOption 2: 10 cmOption 3: 9 cmOption 4: 8 cm

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Question : What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?
Option 1: 7 cm
Option 2: 10 cm
Option 3: 9 cm
Option 4: 8 cm