Note:
Use Q1 and Q2 from Volume of 3D Shapes from GCSE.
Q3
Calculate the volume of the cube below.
Answer: 216 cm^3
Wrong Answers:
36 cm^3
18 cm^3
72 cm^3
WORKING:
To calculate the volume of a cube we do: height \times length \times width
Volume =6\times6\times6=216 cm^3.
Q4
Calculate the volume of the cylinder above.
Use \pi = 3.14.
Answer: 11190.96 cm^3
Wrong Answers:
621.72 cm^3
1952.2008 cm^3
1243.44 cm^3
WORKING:
To calculate the volume of a cylinder we use the formula:
Volume = Area of base \times Length.
Volume = 18^2\times3.14\times11=11190.96 cm^3.
Q5
Calculate the volume of the triangular based prism shown above.
Answer: 280 cm^3
Wrong Answers:
560 cm^3
182 cm^3
13.5 cm^3
WORKING:
The volume of a prism is calculated using the formula:
Volume = Area of base \times Length.
Area of base = \dfrac{1}{2}\times5\times8=20 cm^2>
Volume = 20\times14=280 cm^3.
Q6
Pat drills a circular hole all the way through a block of wood, as shown above.
The diameter of the hole is 8 cm.
What is the volume of the wood that is remaining?
Use \pi = 3.14.
Answer: 1797.12 cm^3
Wrong Answers:
2098.56 cm^3
2349.76 cm^3
2208 cm^3
WORKING:
Volume of the block of wood = 12\times20\times10 = 2400 cm^3.
Volume of the hole = 3.14\times 4^2\times12=602.88 cm^3.
Volume of remaining wood = 2400 cm^3 – 602.88 cm^3 = 1797.12 cm^3.
Q7
The diameter of the sphere shown above is 13 cm.
Using the formula:
Volume of a sphere = \dfrac{4}{3}\pi r^3
Find the volume of this sphere, giving your answer to 2 decimal places.
Use \pi=3.14.
Answer: 1149.76 cm^3
Wrong Answers:
9198.11 cm^3
176.89 cm^3
862.32 cm^3
WORKING:
We know that the diameter of the sphere is 13 cm, therefore we can find the radius by simply dividing the diameter by 2.
Hence, the radius is \dfrac{13}{2}=6.5 cm.
We can then substitute this value into the formula for the volume of a sphere.
Volume = \dfrac{4}{3}\times3.14\times 6.5^3=1149.76 cm^3.
Q8
Below is the diagram for a silo with a total height of 20 m.
The silo is made up of a cylinder and a hemisphere, both with a radius of 5 m.
Using the formula for the volume of a hemisphere, work out the volume of the silo.
Give your answer to 2 decimal places.
Volume of a hemisphere = \dfrac{2}{3}\pi r^3
Use \pi = 3.14.
Answer: 1439.17 m^3
Wrong Answers:
1831.67 m^3
1229.83 m^3
1570 m^3
WORKING:
To calculate the volume of the hemisphere part of the silo we substitute r=5 into the formula given in the question.
Volume of hemisphere = \dfrac{2}{3}\times3.14\times5^3=261.\dot{6}=261.67 m^3.
To calculate the volume of the cylinder part of the silo, we need to multiply the area of the base by the height.
We know that the height of the silo is 20 m and that the radius of the hemisphere is 5 m.
So to find the height of the cylinder we simply take 5 m away from 20 m, to get 15 m.
Then the volume of the cylinder = 3.14\times 5^2 \times 15 = 1177.5 m^3.
Volume of silo = 1177.5 m^3 + 261.67 m^3 = 1439.17 m^3.