Calculate the volume of each prism shown, with dimensions provided for length, width, height, and base measurements.
Diagrams of various prisms with labeled dimensions for volume calculation.
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Show Answer Key & Explanations
Step-by-step solution for: Y9. Shape & Space. Volumes of Prisms & Cylinders - Maths with David
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Show Answer Key & Explanations
Step-by-step solution for: Y9. Shape & Space. Volumes of Prisms & Cylinders - Maths with David
To calculate the volume of each prism, we use the general formula for the volume of a prism:
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
We will solve each part step by step.
---
- Dimensions: \(3 \, \text{cm} \times 4 \, \text{cm} \times 6 \, \text{cm}\)
- Base Area: \(4 \, \text{cm} \times 6 \, \text{cm} = 24 \, \text{cm}^2\)
- Height: \(3 \, \text{cm}\)
- Volume: \(24 \, \text{cm}^2 \times 3 \, \text{cm} = 72 \, \text{cm}^3\)
\[
\boxed{72 \, \text{cm}^3}
\]
---
- Base is a right triangle with legs \(5 \, \text{cm}\) and \(6 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 5 \, \text{cm} \times 6 \, \text{cm} = 15 \, \text{cm}^2\)
- Height (length of the prism): \(20 \, \text{cm}\)
- Volume: \(15 \, \text{cm}^2 \times 20 \, \text{cm} = 300 \, \text{cm}^3\)
\[
\boxed{300 \, \text{cm}^3}
\]
---
- Base is a trapezoid with parallel sides \(4 \, \text{m}\) and \(7 \, \text{m}\), and height \(5 \, \text{m}\)
- Base Area: \(\frac{1}{2} \times (4 \, \text{m} + 7 \, \text{m}) \times 5 \, \text{m} = \frac{1}{2} \times 11 \, \text{m} \times 5 \, \text{m} = 27.5 \, \text{m}^2\)
- Height (length of the prism): Not explicitly given, but assuming it is the same as the slanted side (not necessary for calculation if not provided)
- Volume: \(27.5 \, \text{m}^2 \times \text{height}\) (Assuming height is the same as the slanted side, which is not clear from the image. Let's assume the height is the perpendicular distance between the bases.)
\[
\boxed{27.5 \, \text{m}^2 \times \text{height}}
\]
---
- Dimensions: \(1.1 \, \text{m} \times 40 \, \text{cm} \times 2 \, \text{m}\)
- Convert \(40 \, \text{cm}\) to meters: \(40 \, \text{cm} = 0.4 \, \text{m}\)
- Base Area: \(1.1 \, \text{m} \times 0.4 \, \text{m} = 0.44 \, \text{m}^2\)
- Height: \(2 \, \text{m}\)
- Volume: \(0.44 \, \text{m}^2 \times 2 \, \text{m} = 0.88 \, \text{m}^3\)
\[
\boxed{0.88 \, \text{m}^3}
\]
---
- Base is an equilateral triangle with side \(7 \, \text{cm}\) and height \(8 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 7 \, \text{cm} \times 8 \, \text{cm} = 28 \, \text{cm}^2\)
- Height (length of the prism): \(5.5 \, \text{cm}\)
- Volume: \(28 \, \text{cm}^2 \times 5.5 \, \text{cm} = 154 \, \text{cm}^3\)
\[
\boxed{154 \, \text{cm}^3}
\]
---
- Base is a trapezoid with parallel sides \(6 \, \text{cm}\) and \(9 \, \text{cm}\), and height \(6 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times (6 \, \text{cm} + 9 \, \text{cm}) \times 6 \, \text{cm} = \frac{1}{2} \times 15 \, \text{cm} \times 6 \, \text{cm} = 45 \, \text{cm}^2\)
- Height (length of the prism): \(12 \, \text{cm}\)
- Volume: \(45 \, \text{cm}^2 \times 12 \, \text{cm} = 540 \, \text{cm}^3\)
\[
\boxed{540 \, \text{cm}^3}
\]
---
- Base is a rectangle with dimensions \(5 \, \text{cm} \times 12 \, \text{cm}\)
- Base Area: \(5 \, \text{cm} \times 12 \, \text{cm} = 60 \, \text{cm}^2\)
- Height (length of the prism): \(22 \, \text{cm}\)
- Volume: \(60 \, \text{cm}^2 \times 22 \, \text{cm} = 1320 \, \text{cm}^3\)
\[
\boxed{1320 \, \text{cm}^3}
\]
---
- Base is a trapezoid with parallel sides \(25 \, \text{cm}\) and \(40 \, \text{cm}\), and height \(8 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times (25 \, \text{cm} + 40 \, \text{cm}) \times 8 \, \text{cm} = \frac{1}{2} \times 65 \, \text{cm} \times 8 \, \text{cm} = 260 \, \text{cm}^2\)
- Height (length of the prism): \(10 \, \text{cm}\)
- Volume: \(260 \, \text{cm}^2 \times 10 \, \text{cm} = 2600 \, \text{cm}^3\)
\[
\boxed{2600 \, \text{cm}^3}
\]
---
- Base is a triangle with base \(14 \, \text{cm}\) and height \(9 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 14 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2\)
- Height (length of the prism): \(11 \, \text{cm}\)
- Volume: \(63 \, \text{cm}^2 \times 11 \, \text{cm} = 693 \, \text{cm}^3\)
\[
\boxed{693 \, \text{cm}^3}
\]
---
\[
\boxed{72, 300, 27.5 \times \text{height}, 0.88, 154, 540, 1320, 2600, 693}
\]
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
We will solve each part step by step.
---
(a) Rectangular Prism
- Dimensions: \(3 \, \text{cm} \times 4 \, \text{cm} \times 6 \, \text{cm}\)
- Base Area: \(4 \, \text{cm} \times 6 \, \text{cm} = 24 \, \text{cm}^2\)
- Height: \(3 \, \text{cm}\)
- Volume: \(24 \, \text{cm}^2 \times 3 \, \text{cm} = 72 \, \text{cm}^3\)
\[
\boxed{72 \, \text{cm}^3}
\]
---
(b) Triangular Prism
- Base is a right triangle with legs \(5 \, \text{cm}\) and \(6 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 5 \, \text{cm} \times 6 \, \text{cm} = 15 \, \text{cm}^2\)
- Height (length of the prism): \(20 \, \text{cm}\)
- Volume: \(15 \, \text{cm}^2 \times 20 \, \text{cm} = 300 \, \text{cm}^3\)
\[
\boxed{300 \, \text{cm}^3}
\]
---
(c) Trapezoidal Prism
- Base is a trapezoid with parallel sides \(4 \, \text{m}\) and \(7 \, \text{m}\), and height \(5 \, \text{m}\)
- Base Area: \(\frac{1}{2} \times (4 \, \text{m} + 7 \, \text{m}) \times 5 \, \text{m} = \frac{1}{2} \times 11 \, \text{m} \times 5 \, \text{m} = 27.5 \, \text{m}^2\)
- Height (length of the prism): Not explicitly given, but assuming it is the same as the slanted side (not necessary for calculation if not provided)
- Volume: \(27.5 \, \text{m}^2 \times \text{height}\) (Assuming height is the same as the slanted side, which is not clear from the image. Let's assume the height is the perpendicular distance between the bases.)
\[
\boxed{27.5 \, \text{m}^2 \times \text{height}}
\]
---
(d) Rectangular Prism
- Dimensions: \(1.1 \, \text{m} \times 40 \, \text{cm} \times 2 \, \text{m}\)
- Convert \(40 \, \text{cm}\) to meters: \(40 \, \text{cm} = 0.4 \, \text{m}\)
- Base Area: \(1.1 \, \text{m} \times 0.4 \, \text{m} = 0.44 \, \text{m}^2\)
- Height: \(2 \, \text{m}\)
- Volume: \(0.44 \, \text{m}^2 \times 2 \, \text{m} = 0.88 \, \text{m}^3\)
\[
\boxed{0.88 \, \text{m}^3}
\]
---
(e) Triangular Prism
- Base is an equilateral triangle with side \(7 \, \text{cm}\) and height \(8 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 7 \, \text{cm} \times 8 \, \text{cm} = 28 \, \text{cm}^2\)
- Height (length of the prism): \(5.5 \, \text{cm}\)
- Volume: \(28 \, \text{cm}^2 \times 5.5 \, \text{cm} = 154 \, \text{cm}^3\)
\[
\boxed{154 \, \text{cm}^3}
\]
---
(f) Trapezoidal Prism
- Base is a trapezoid with parallel sides \(6 \, \text{cm}\) and \(9 \, \text{cm}\), and height \(6 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times (6 \, \text{cm} + 9 \, \text{cm}) \times 6 \, \text{cm} = \frac{1}{2} \times 15 \, \text{cm} \times 6 \, \text{cm} = 45 \, \text{cm}^2\)
- Height (length of the prism): \(12 \, \text{cm}\)
- Volume: \(45 \, \text{cm}^2 \times 12 \, \text{cm} = 540 \, \text{cm}^3\)
\[
\boxed{540 \, \text{cm}^3}
\]
---
(g) Rectangular Prism
- Base is a rectangle with dimensions \(5 \, \text{cm} \times 12 \, \text{cm}\)
- Base Area: \(5 \, \text{cm} \times 12 \, \text{cm} = 60 \, \text{cm}^2\)
- Height (length of the prism): \(22 \, \text{cm}\)
- Volume: \(60 \, \text{cm}^2 \times 22 \, \text{cm} = 1320 \, \text{cm}^3\)
\[
\boxed{1320 \, \text{cm}^3}
\]
---
(h) Trapezoidal Prism
- Base is a trapezoid with parallel sides \(25 \, \text{cm}\) and \(40 \, \text{cm}\), and height \(8 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times (25 \, \text{cm} + 40 \, \text{cm}) \times 8 \, \text{cm} = \frac{1}{2} \times 65 \, \text{cm} \times 8 \, \text{cm} = 260 \, \text{cm}^2\)
- Height (length of the prism): \(10 \, \text{cm}\)
- Volume: \(260 \, \text{cm}^2 \times 10 \, \text{cm} = 2600 \, \text{cm}^3\)
\[
\boxed{2600 \, \text{cm}^3}
\]
---
(i) Triangular Prism
- Base is a triangle with base \(14 \, \text{cm}\) and height \(9 \, \text{cm}\)
- Base Area: \(\frac{1}{2} \times 14 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2\)
- Height (length of the prism): \(11 \, \text{cm}\)
- Volume: \(63 \, \text{cm}^2 \times 11 \, \text{cm} = 693 \, \text{cm}^3\)
\[
\boxed{693 \, \text{cm}^3}
\]
---
Final Answers:
\[
\boxed{72, 300, 27.5 \times \text{height}, 0.88, 154, 540, 1320, 2600, 693}
\]
Parent Tip: Review the logic above to help your child master the concept of volumes of prisms and cylinders worksheet.
