Topic 2 Volume - Big Ideas Learning · PDF file 2011-02-02 · Volume 403 EXAMPLE 2...

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Transcript of Topic 2 Volume - Big Ideas Learning · PDF file 2011-02-02 · Volume 403 EXAMPLE 2...

  • 402 Additional Topics

    Lesson Tutorials

    Find the volume of the solid. Round your answer to the nearest tenth.

    a. V = Bh Write formula for volume of a cylinder.

    = π (8)2(4) Substitute.

    = 256π ≈ 803.8 Simplify.

    The volume is about 803.8 cubic centimeters.

    b. V = 1 — 3

    Bh Write formula for volume of a cone.

    = 1 — 3

    π (3)2(5) Substitute.

    = 15π ≈ 47.1 Simplify.

    The volume is about 47.1 cubic feet.

    EXAMPLE Finding the Volume of a Cylinder and a Cone11

    VolumeTopic 2

    Volume of a Cylinder

    Words The volume V of a cylinder is the product of the area of the base and the height of the cylinder.

    Algebra V = Bh = π r 2h

    Volume of a Cone

    Words The volume V of a cone is one-third the product of the area of the base and the height of the cone.

    Algebra V = 1

    — 3

    Bh = 1

    — 3

    π r 2h

    Area of base

    Height of cylinder

    Height of cone

    area of base, B

    height, h

    height, h

    area of base, B

    8 cm

    4 cm

    3 ft

    5 ft

    Area of base

    Remember Pi can be approximated

    as 3.14 or 22

    — 7 .

    MSCC8PE2_AT_02.indd 402MSCC8PE2_AT_02.indd 402 11/29/10 8:59:58 AM11/29/10 8:59:58 AM

    www.bigideasmath.com/protected/content/ipe_cc/grade%208/extra_help/at/lt_at_02.html

  • Volume 403

    EXAMPLE Finding the Volume of a Sphere22 The globe of the moon has a radius of 10 inches. Find the volume of the globe. Round your answer to the nearest whole number.

    V = 4 — 3

    πr 3 Write formula for volume of a sphere.

    = 4 — 3

    π (10)3 Substitute.

    = 4000 — 3

    π ≈ 4187 Simplify.

    The volume of the globe is about 4187 cubic inches.

    Find the volume of the solid. Round your answer to the nearest tenth.

    1.

    7 m

    6 m 2. 10 ft

    4 ft

    3. 5 in.

    2 in.

    4.

    9.5 yd

    12 yd 5.

    4 cm

    6.

    16 ft

    7. PACKAGING A cylindrical container of three rubber balls has a height of 18 centimeters and a diameter of 6 centimeters. Each ball in the container has a radius of 3 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.

    Volume of a Sphere

    Words The volume V of a sphere is the

    product of 4

    — 3

    π and the cube of

    the radius of the sphere.

    Algebra V = 4

    — 3

    π r3

    radius, r

    Cube of radius of sphere

    MSCC8PE2_AT_02.indd 403MSCC8PE2_AT_02.indd 403 11/29/10 9:00:00 AM11/29/10 9:00:00 AM

    English_on: English_off: Spanish_on: Spanish_off: text1: English text2: Spanish