Volume of a Cone and Pyramid

Volume of a Cone and Pyramid
Calculate the volume of the cone.
Calculate the volume of the frustum.
9 π‘π‘š
3π‘š
The volumes of the cone and cylinder are
equal to each other. Write an expression for
the height of the cone in terms of π‘₯.
π‘₯
10π‘š
4π‘₯
β„Ž
4 π‘π‘š
7π‘š
12π‘š
2π‘₯
Calculate the volume of the cone.
20 π‘π‘š
11 π‘š
Calculate the volume of the square based
pyramid.
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Volume of a Cone and Pyramid
Answers
Calculate the volume of the cone.
7π‘š
9 π‘π‘š
12π‘š
πœ‹ × 42 × 9
𝑉=
3
𝑉 = 150.8π‘π‘š3 (1 𝑑𝑝)
Calculate the volume of the frustum.
πœ‹ × 32 × 5
𝑉𝑠 =
= 15πœ‹
3
3π‘š
πœ‹ × 102 × 12
𝑉𝐿 =
= 400πœ‹
3
𝑉 = 𝑉𝐿 βˆ’ 𝑉𝑠 = 400πœ‹ βˆ’ 15πœ‹
= 385πœ‹ = 1209.5π‘š3 (1𝑑𝑝)
10π‘š
β„Ž
4 π‘π‘š
The volumes of the cone and cylinder are
equal to each other. Write an expression for
the height of the cone in terms of π‘₯.
1
π‘₯
𝑉 = πœ‹ 2π‘₯ 2 β„Ž
3
4πœ‹π‘₯ 2 β„Ž
4π‘₯
=
3
11 π‘š
2
6 × 11
3
𝑉 = 132π‘π‘š3
𝑉=
Calculate the volume of the cone.
20 π‘π‘š
Calculate the volume of the square based
pyramid.
π‘Ÿ = 252 βˆ’ 202
π‘Ÿ = 225
π‘Ÿ = 15π‘π‘š
πœ‹ × 152 × 20
𝑉=
3
= 1500πœ‹
= 4712.4π‘π‘š3 (1𝑑𝑝)
2π‘₯
∴
4πœ‹π‘₯ 2 β„Ž
= 4π‘₯ 3 πœ‹
3
4πœ‹π‘₯ 2 β„Ž = 12π‘₯ 3 πœ‹
12π‘₯ 3 πœ‹
β„Ž=
4πœ‹π‘₯ 2
𝒉 = πŸ‘π’™
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𝑉 = πœ‹π‘₯ 2 × 4π‘₯
= 4π‘₯ 3 πœ‹