A solid is a hemisphere of radius r surmounted by a cone of the same radius. The total height of the solid is 3r. Find the cone's volume as a fraction of the total solid's volume.

Question

Accepted Answer

1/2. Total height 3r = cone height + r (hemisphere). So cone height = 2r. Cone = 1/3 π r^2 (2r) = 2/3 π r^3. Hemisphere = 2/3 π r^3. They are equal, so cone is 1/2 of the total.

A solid is a hemisphere of radius $r$ surmounted by a cone of the same radius. The total height of the solid is $3 r$ .
Find the cone's volume as a fraction of the total solid's volume.

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More Class 10 Volume of Combined Solids practice

A solid is a hemisphere of radius r surmounted by a cone of the same radius. The total height of the solid is 3r.Find the cone's volume as a fraction of the total solid's volume.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Volume of Combined Solids practice

A solid is a hemisphere of radius $r$ surmounted by a cone of the same radius. The total height of the solid is $3 r$ .
Find the cone's volume as a fraction of the total solid's volume.