By: Shelbi Legg and Taylor Mastin

Find volumes of prisms. Find volumes of cylinders.

The volume of a figure is the measure of the amount of space that a figure encloses.

Volume is measured in cubic units.

(units³) You can create a rectangular

prism from different views of the figure to investigate its volume.

If a prism has a volume of V cubic units, a height of h units, and each base has an area of B square units, then V=Bh.

Area of Base=B

h

a

8 cm

17 cm

13 cm

Find the volume of the

triangular prism.

a² + b² = c² Use Pythagoream Theorem. a² + 8² = 17² b=8, c=17 a² + 64 = 289 Multiply. a² = 225 Subtract 64 from both

sides. a = 15 Take the square root of

both sides. V= Bh Next, find the volume of the

prism. V=½(8)(15)(13) Substitute the numbers in. V=780 cm³ Multiply.

Find the volume of

the rectangular

prism.

8(3)= 24 Find the area of the base. V= 24(12) Then plug the area of the

base into the formula. V= 288 in³ Multiply.

If a cylinder has a volume of V cubic units, a height of h units, and the bases have radii of r units, then V=Bh or V=πr²h. Area of base= πr²

r

Find the volume of the cylinder.

r= 4.6 m

h=12.4

V= ¶r²h Use the volume formula for cylinders. V= ¶(4.6²)(12.4) r= 4.6 m, h= 12.4 m V≈824.3 m³ Multiply.

R= 4.6

12.4

If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

If a cylinder has a base with an area of B square units and a height of h units, then its volume is Bh cubic units, whether it is right or oblique.

h

Find the volume of the oblique cylinder.

4 yd

9 yd

V= ¶r²h Use the formula for a right cylinder.

V=¶(4²)(9) r=4 yd, h=9 yd V= 452.4 yd³

9

4

Pg. 692 #7-24