Volume of Prisms and Cylinders Measured in cubic units3

CUBE Here is a 3-dimensional view of a cube CUBE Here is a 3-dimensional view of a cube. The view on the left is the cube. The view on the right shows the base of the cube. The formula for the volume of a cube: V = Bh V = lwh

Find the volume of the cube V = Bh or V =lwh V = 5 · 5 · 5 or 53 V = 125 units3 The volume of the cube is 125 units3. Volume is measured in cubic units.

A die is a cube molded from hard plastic A die is a cube molded from hard plastic. The edge of a typical die measure 0.62 inches. Dice are usually produced in a mold which holds 100 die at a time. To the nearest cubic inch, how much plastic is needed to fill this large mold? When working with word problems, be sure to read carefully to determine what the question wants you to find. This question clearly indicates that you are to compute the volume by stating “to the nearest cubic inch.” Volume of one die = lwh = (.62)(.62)(.62) = 0.238 cubic inches For 100 dice = 23.8 = 24 cubic inches

Volumes of Prisms and Cylinders A prism is a three-dimensional figure named for the shape of its bases. Triangular prism has triangles for bases. Rectangular prism has rectangles for bases. If all six faces of a prism are squares, it is a cube.

Rectangular prism In this rectangular prism the two bases are rectangles. The volume formula is V = Bh V = (lw)h length · width · height

Find the volume of the prism V = Bh or V = lwh V = 12 · 8 · 3 V = 288 in3 The volume of the prism is 288 in3. Volume is measured in cubic units.

Triangular prism In this triangular prism the two bases are triangles. The formula for volume of a triangular prism is V = Bh, where B is area of the base and h is height.

Here is another view of a triangular prism Here is another view of a triangular prism. The view on the left shows you how the prism looks in a 3-dimensional view. The view on the right is the base of the prism.

Find the volume of the prism V = Bh B = area of the base = area of a triangle V = ½ bh · h V = (.5)(16)(12) = 96 in2 V = Bh height = 12 in V = 96 · 12 V = 1152 in3 Volume of the prism is 1152 in3. Volume is measured in cubic units. Find the volume of the prism

Cylinder: a cylinder is a three-dimensional figure with two circular bases. The volume of a cylinder is the area of the base B times the height h. V = Bh or V = (πr²)h

Find the volume of the cylinder V = Bh or V = πr2h V = (π · 42) · 10 V = 502.4 cm3 The volume of the cylinder is 502.4 cm3. Volume is measured in cubic units.

A practical application Finding Volumes A practical application

Find the volume of the cylinder to the nearest tenth Find the volume of the cylinder to the nearest tenth. V = Bh V = πr2 · h V = 3.14 · 32 · 8.6 V = 243.036 cm3 V = 243 cm3

Find the volume of the prism to the nearest tenth V = Bh V = 6 · 8 · 2 V = 96 cm3

Find the volume of the triangular prism V = Bh V = ½bh · h V = ½(12 · 16) · 12 V = ½(192) · 12 V = ½(2304) V = 1152 in3