Question

area, volume and capacity
topic 5: volume of a cube
question 1 find the volume of the following cubes.
question 2
a the volume of a cube is 125 cm³. what is the length of each edge?
b the volume of a cube is 343 cm³. find its side length.
question 3 calculate the volume of each of the following cubes whose side length is given. show all your working.
a 1 cm b 11 cm c 10 cm
d 2.4 m e 3 m f 1.6 m
g 8 cm h 1.9 m i 2.5 m
area, volume and capacity

Explanation:

Question 2a

Step1: Recall the formula for the volume of a cube

The volume formula of a cube is \(V = s^{3}\), where \(s\) is the side - length. Given \(V = 125\mathrm{cm}^{3}\), we need to find \(s\).

Step2: Solve for \(s\)

We know that \(s=\sqrt[3]{V}\). Substituting \(V = 125\mathrm{cm}^{3}\), since \(5\times5\times5=125\), then \(s = 5\mathrm{cm}\).

Question 2b

Step1: Use the volume formula of a cube

Using \(V = s^{3}\), with \(V = 343\mathrm{cm}^{3}\).

Step2: Calculate the side - length

We find \(s=\sqrt[3]{V}\). Because \(7\times7\times7 = 343\), so \(s=7\mathrm{cm}\).

Question 3a

Step1: Apply the volume formula

For a cube with \(s = 1\mathrm{cm}\), \(V=s^{3}\).

Step2: Compute the volume

\(V=1^{3}=1\times1\times1 = 1\mathrm{cm}^{3}\).

Question 3b

Step1: Use the volume formula

For \(s = 11\mathrm{cm}\), \(V=s^{3}\).

Step2: Calculate the volume

\(V = 11^{3}=11\times11\times11=1331\mathrm{cm}^{3}\).

Question 3c

Step1: Apply the volume formula

For \(s = 10\mathrm{cm}\), \(V=s^{3}\).

Step2: Find the volume

\(V=10^{3}=10\times10\times10 = 1000\mathrm{cm}^{3}\).

Question 3d

Step1: Use the volume formula

For \(s = 2.4\mathrm{m}\), \(V=s^{3}\).

Step2: Calculate the volume

\(V=(2.4)^{3}=2.4\times2.4\times2.4=13.824\mathrm{m}^{3}\).

Question 3e

Step1: Apply the volume formula

For \(s = 3\mathrm{m}\), \(V=s^{3}\).

Step2: Compute the volume

\(V=3^{3}=3\times3\times3=27\mathrm{m}^{3}\).

Question 3f

Step1: Use the volume formula

For \(s = 1.6\mathrm{m}\), \(V=s^{3}\).

Step2: Calculate the volume

\(V=(1.6)^{3}=1.6\times1.6\times1.6 = 4.096\mathrm{m}^{3}\).

Question 3g

Step1: Apply the volume formula

For \(s = 8\mathrm{cm}\), \(V=s^{3}\).

Step2: Find the volume

\(V=8^{3}=8\times8\times8=512\mathrm{cm}^{3}\).

Question 3h

Step1: Use the volume formula

For \(s = 1.9\mathrm{m}\), \(V=s^{3}\).

Step2: Calculate the volume

\(V=(1.9)^{3}=1.9\times1.9\times1.9=6.859\mathrm{m}^{3}\).

Question 3i

Step1: Apply the volume formula

For \(s = 2.5\mathrm{m}\), \(V=s^{3}\).

Step2: Compute the volume

\(V=(2.5)^{3}=2.5\times2.5\times2.5 = 15.625\mathrm{m}^{3}\).

Answer:

• Question 2a: \(5\mathrm{cm}\)
• Question 2b: \(7\mathrm{cm}\)
• Question 3a: \(1\mathrm{cm}^{3}\)
• Question 3b: \(1331\mathrm{cm}^{3}\)
• Question 3c: \(1000\mathrm{cm}^{3}\)
• Question 3d: \(13.824\mathrm{m}^{3}\)
• Question 3e: \(27\mathrm{m}^{3}\)
• Question 3f: \(4.096\mathrm{m}^{3}\)
• Question 3g: \(512\mathrm{cm}^{3}\)
• Question 3h: \(6.859\mathrm{m}^{3}\)
• Question 3i: \(15.625\mathrm{m}^{3}\)