Ch 12.3

S = Ph + 2B = (2π)(1.25) × (5) + 2(π)(1.252) = 15.625π

L = Ph = (2π)(5) × (4) = 40π

Find the lateral area of the cylinder.

Find the surface area of the cylinder.

Find the surface area of the prism.

S = Ph + 2B = (4×6)(5) + 2(3)[(4×6)]/2 = 192

3

Ch 12.3Volumes of

Prisms & Cylinders

Standard 9.0Students compute the volumes of prisms and cylinders and commit to memory the formulas

for prisms and cylinders.

Learning Target:I will be able to solve problems involving volumes of prisms and cylinders.

Ch 10.5Ch 12.3

Theorem 12-5

Ch 10.5Ch 12.3

Volume of a Prism

Answer: The volume of the prism is 1500 cubic cm.

V Bh Volume of a prism

1500 Simplify.

Find the volume of the prism.

Ch 10.5Ch 12.3

A. 6480 in3

B. 8100 in3

C. 3240 in3

D. 4050 in3

Find the volume of the prism.

Ch 10.5Ch 12.3

Volume of a prism

B = (18×a)/2 , a = √(302 – 182), h = 15

Multiply.

= (216) (15)

= 3240

V = Bh

Ch 10.5Ch 12.3

Theorem 12-6

Volume of a Cylinder

Find the volume of the cylinder in terms of π.

Answer: The volume is approximately 18.3 cm3.

B = π r2

= 5.832π Simplify.

= (1.8)2(1.8) r = 1.8 and h = 1.8

Ch 10.5Ch 12.3

Volume of a cylinderV = Bh

A. 20π cm3

B. 200π cm3

C. 40π cm3

D. 320π cm3

Find the volume of the cylinder in terms of π.

Ch 10.5Ch 12.3

Volume of a prism

B = π r2, r = 8 , h = 5

Multiply.

= π (82) (5)

= 320π

V = Bh

Ch 10.5Ch 12.3

Volume of an Oblique Solid

Find the volume of the oblique cylinder in terms of π.

To find the volume, use the formula for a right cylinder.

Answer: The volume is approximately 17,671.5 feet3.

B = π r2

r 15, h 25

Ch 10.5Ch 12.3

Volume of a cylinderV = Bh

= 5625π Multiply.

A. 484π cm3

B. 5322π cm3

C. 1694π cm3

D. 2661π cm3

Find the volume of the oblique cylinder to the nearest tenth.

Ch 10.5Ch 12.3

Volume of a cylinder

B = π r2, r = 11 , h = 44

Multiply.

= π (112) (44)

= 5322π

V = Bh

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A,what is the length of each prism?

Prism A Prism B

Ch 10.5Ch 12.3

Read the Test Item

You know the volume of each solid and that the difference between their volumes is 128 cubic inches.

Solve the Test Item

VB – VA = 128 Difference of Volumes

(4x ● 9) – (4x ● 5) = 128 Use V = Bh.

16x = 128 Simplify.

x = 8 Divide each side by 16.

Answer: The length of each prism is 8 inches.

Ch 10.5Ch 12.3

Prism A Prism B

A. 4 in.

B. 6 in.

C. 8 in.

D. 10.5 in.

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A,what is the length of each prism?

Prism A

Prism B

Ch 10.5Ch 12.3

VB - VA = Vdifference

VB – VA = 128 Difference of Volumes

(6x ● 7) – (6x ● 11) = 192 Use V = Bh.

24x = 192 Simplify.x = 8