Question

Can someone help me get the understanding on the formula for volume for a cylinder and a sphere?

Answer 1

Answer:

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Answer 2

Answer:

A cylinder is a solid composed of two congruent circles in parallel planes, their interiors, and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions.

The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( in3,ft3,cm3,m3 , et cetera). Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a cylinder with radius r is the area of the base B times the height h .

V=Bh  or  V=πr2h

Example:

Find the volume of the cylinder shown. Round to the neatest cubic centimeter.

Solution

The formula for the volume of a cylinder is V=Bh  or  V=πr2h .

The radius of the cylinder is 8 cm and the height is 15 cm.

Substitute 8 for r and 15 for h in the formula V=πr2h .

V=π(8)2(15)

Simplify.

V=π(64)(15)≈3016

Therefore, the volume of the cylinder is about 3016 cubic centimeters.

A sphere is a set of points in space that are a given distance r from the center

The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units( in3,ft3,cm3,m3 , et cetera). Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a sphere is four-thirds times pi times the radius cubed.

V=43πr3

The volume of a hemisphere is one-half the volume of the related sphere.

Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

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Volume of a Sphere

A sphere is a set of points in space that are a given distance r from the center.

The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units( in3,ft3,cm3,m3 , et cetera). Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a sphere is four-thirds times pi times the radius cubed.

V=43πr3

The volume of a hemisphere is one-half the volume of the related sphere.

Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

Example:

Find the volume of the sphere. Round to the nearest cubic meter.

Solution

The formula for the volume of a sphere is

V=43πr3

From the figure, the radius of the sphere is 8 m.

Substitute 8 for r in the formula.

V=43π(8)3

Simplify.

V=43π(512)

≈2145

Therefore, the volume of the sphere is about 2145 m3 .

Hope it helps you....

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