Page 22 - Math Course 2 (Book 2)

Geometric Volume: Prisms and Cylinders

Volume of an Oblique Cone
Let’s Begin
Examples

Volume of a Pyramid Find the volume of the oblique cone to the
nearest tenth.
Examples Use trigonometry to find the radius of the base.

CLOCKS
Theo has a clock that is in the shape of a square
pyramid. The clock has a base of 3 inches and a
height of 7 inches. Find the volume of the clock.
25 ft
1 Volume of a
V = Bh 70°
3 pyramid
1 2 2
= S h B = s 7 in.
3
1 2
= (3 )(7) s = 3, h = 7 opposite
3
tan A = adjacent Definition of tangent
= 21 Multiply.
25 A = 70°, opposite = 25,
tan 70° =
r and adjacent = r.
3 in.
r = 25 Solve for r.
tan 70°
The volume of the clock is 21
Answer
cubic inches. r ≈ 9.1 Use a calculator.

Volume of a Cone Now find the volume.

1
Examples = πr h Volume of a cone
2
3
1 2
3
Find the volume of the cone to the nearest tenth. ≈ π(9.1 )(25) r ≈ 9.1, h = 25
5 in.
≈ 2167.6 Use a calculator.

The volume of the cone is
12 in. Answer
approximately 2167.6 cubic feet.

1
2
V = πr h Volume of a cone
3
1
2
= π(5) 12 r = 5, h = 12
3
≈ 314.1 Use a calculator
The volume of the cone is
Answer approximately 314.1 cubic
inches.

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