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The width, height, and length of a box or rectangular prism can be different. If all three are the same, then the box is a cube.

Rectangular Prism

• The volume, or the amount of space inside a box, is h × w × l.

• The surface area of a box is 2(h × w) + 2(h × l) + 2(w × l)

• A shoe box is a rectangular prism with a volume of 6287 cm3

Geometry

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Rectangular PrismFind the volume of this jewelry box by

using the equation for a rectangular prism:

Dimensions of the Jewelry Box: Height = 14 cm Length = 30 cm Width = 18 cm

(ANSWER: 14 x 30 x 18 = 7,560 cm3)

3

The radius, r, or the distance from the center of a sphere to its edge, is the defining property of a sphere.

Sphere• The diameter, or the distance across a sphere that passes

through the center point, is 2r (twice the radius). • The surface area of a sphere is 4r2. • The volume enclosed by a sphere is 4/3r3. • Note that =3.1415926535. • A basketball has a volume of 7700cm3 .

Geometry

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Sphere Find the volume of this basketball by

using the equation for a sphere:

Dimensions of the Basketball: Radius = 11.9 cm

(ANSWER: 4/3 x 3.14 x 11.9 x 11.9 x 11.9 = 7,055 cm3)

5

GeometryThe radius, r, is thedistance from the center of a cone to its edge.

The height, h, is the distance from the tip of the cone to the center of the base of the cone.

Cone The diameter, or the distance across the base of the cone

through the center, is 2r (twice the radius). The surface area of a cone is r h2 + r 2 + r 2.

The volume of a cone is 1/3 r 2 h. Note that =3.1415926535! But you can round to the hundredths place and use 3.14.

An ice cream cone is a cone with a volume of 180cm3.

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Cone Find the volume of this ice cream cone

by using the equation for a cone:

Dimensions of the Ice Cream Cone: Radius = 3.5 cm Height = 14 cm

(ANSWER: 1/3 x 3.14 x 3.5 x 3.5 x 14 = 179.5 cm3)

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Geometry If your cylinder is The radius, r, is the standing upright, you distance from the might call the “length”, center of a cylinder l, a "height" instead. to its edge.

Cylinder• The diameter, or the distance across a cylinder that

passes through the center point, is 2r (twice the radius). • The surface area of an open ended cylinder (as shown)

is 2r l . • If the cylinder has caps on the ends, then the surface

area is 2r l +2r2. • The volume of a cylinder is r2 l .• A soda can has a volume of 335 cm3 .

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Cylinder Find the volume of this spray can by

using the equation for a cylinder:

Dimensions of the Spray Can:Radius = 10 cm Length = 50 cm

(ANSWER: 3.14 x 10 x 10 x 50 = 15,700 cm3)