Volume of Prisms & Volume of Prisms & CylindersCylinders

Look at the three shapes I Look at the three shapes I have and tell me what have and tell me what they have in common they have in common when one is trying to when one is trying to calculate the volume of calculate the volume of these figures.these figures.

ANSWER(S)ANSWER(S)

►All figures have a base which All figures have a base which the the areaarea must be calculated must be calculated and multiplied by the and multiplied by the heightheight of of the shape so to find the the shape so to find the volume……volume……

V = V = BBhh

Common Core #24Common Core #24►Find the Volume of Find the Volume of Prisms and CylindersPrisms and Cylinders

►(1) Rectangular Prisms(1) Rectangular Prisms►(2) Triangular Prisms(2) Triangular Prisms►(3) Cylinders(3) Cylinders

Find the Volume of the Rectangular Find the Volume of the Rectangular PrismPrism

5in

3in

10inV = Bh or V= lwh

= (3in • 5in)(10in)

= (15in2)(10in)

= 150in3

Area of Base

B = l•w

Find the volume of a Triangular PrismFind the volume of a Triangular Prism

20m

29m

40m

V = Bh

V = ½lw • h

= ½(20m)(21m) • (40m)

= 210m2 • 40m

= 8400m3

Height of the base:

21m

Triangle

Find the Volume of a Triangular Find the Volume of a Triangular PrismPrism

8in

10in

V = Bh

= ½lw • h

= ½(8in)(7in) • (10in)

≈ (28in2) • (10in)

≈ 280in3

7in

Volume of a CylinderVolume of a Cylinder

r

h

V = Bh

Volume of right cylinder

Height of cylinder

Area of base: (Circle)

A = r2

Volume of a CylinderVolume of a Cylinder

►V = V = BBhh

►V = V = rr22 • h• h

►= (3.14)(5cm)= (3.14)(5cm)22 • (13cm) • (13cm)

►V V = 1020.5cm= 1020.5cm33 or or

►V = 325V = 325cmcm3 3

5cm

13cm

Find the area of the following cylinder.Find the area of the following cylinder.

16ft

9ft

V = Bh

= r2 • h

= (3.14)(8ft)2 • (9ft)

= 1808.64ft3

Area of a Circle

PRACTICE PROBLEMSPRACTICE PROBLEMS