Find the surface area of each.

S = (Pℓ)/2 + B = (20×3)(15)/2 + 20√(102+202)/2 = 623.2 in2

S = (Pℓ)/2 + B = (10×6)(14)/2 + (8.7)(10×6)/2 = 679.8 ft2

8.7

S = (Pℓ)/2 + B = 2π(8)(√(152+82)/2 + π(82) = 200π ft2

S = (Pℓ)/2 + B = 2π(√(82-62)(8)/2 + π(6.92) = 70.3π m2

Ch 12.5Volumes of

Pyramids & Cones

Standard 9.0Students compute the volumes of pyramids and cones and commit to memory the formulas for

pyramids.

Learning Target:I will be able to solve problems involving the volume of pyramids and cones.

Theorem 12-11

Volume of a Pyramid

Find the volume of the square pyramid.

Answer: The volume of the pyramid is 21 cubic inches.

Volume of a pyramid

Multiply. 21

s 3, h 7

Brad is building a model pyramid for a social studies project. The model is a square pyramid with a base edge of 8 feet and a height of 6.5 feet. Find the volume of the pyramid.

A. 416 ft3

B.

C.

D.

Volume of a pyramid

B = s2 , s = 8 , h = 6.5

Multiply.

= (64)(6.5)

= 138.7

V = Bh1313

Theorem 12-12

Volume of a Cone

A. Find the volume of the oblique cone in terms of π.

Simplify

B = π r2

r = 9.1, h = 25

= 690π

Volume of a coneV = Bh13

Volume of a Cone

B. Find the volume of the cone in terms of π.

Simplify.

Volume of a cone

r = 5, h = 12

= 100π

B = π r2

V = Bh13

A. 141π m3

B. 8746π m3

C. 112π m3

D. 2915π m3

A. Find the volume of the oblique cone in terms of π.

Volume of a cone

B = π r2 , r = 20.6 , h = 20.6

Multiply.

= π(424.36)(20.6)

= 2915π

V = Bh1313

A. 960π m3

B. 40π m3

C. 320π m3

D. 880π m3

B. Find the volume of the cone in terms of π.

Volume of a cone

B = π r2 , r = 8 , h = 15

Multiply.

= π(64)(15)

= 320π

V = Bh1313

Find Real-World Volumes

SCULPTURE At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Volume of a pyramid

B = 36 ● 36, h = 52.5

Simplify.

= s2 h13

B = s2

A. 18,775 cm3

B. 19,500 cm3

C. 20,050 cm3

D. 21,000 cm3

SCULPTURE In a botanical garden is a silver pyramidion in the shape of a square pyramid. This pyramid has a height of 65 centimeters and the base edges are 30 centimeters. What is the volume of the pyramidion? Round to the nearest tenth.

Volume of a pyramid

B = s2 , s = 30 , h = 65

Multiply.

= π(900)(65)

= 19500

V = Bh1313