Volume of prisms
Calculate the volume of rectangular and triangular prisms, and find a missing dimension given the volume.
Worked examples
Volume of a rectangular prism
Straightforward
Problem
Find the volume of a rectangular prism with length cm, width cm and height cm.
1
Write the formula for the volume of a rectangular prism.
2
Substitute the length, width and height into the formula.
3
Multiply to calculate the volume.
Answer
Volume of a triangular prism
Moderate
Problem
A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The length of the prism is cm. Find the volume.
1
Find the area of the triangular cross-section using .
2
Multiply the cross-sectional area by the length of the prism.
3
Calculate the volume.
Answer
Finding a missing dimension
Challenging
Problem
A rectangular prism has a volume of cm³, a length of cm and a width of cm. Find the height.
1
Write the formula for the volume of a rectangular prism.
2
Substitute the known values into the formula.
3
Solve for by dividing both sides by .
Answer
Practise
Q1·Straightforward
Find the volume of a rectangular prism with length cm, width cm and height cm.
Explanation
Q2·Straightforward
Find the volume of a rectangular prism with length cm, width cm and height cm.
Explanation
Q3·Straightforward
Find the volume of a rectangular prism with length m, width m and height m.
Explanation
Q4·Straightforward
Find the volume of a rectangular prism with length m, width m and height m.
Explanation
Q5·Moderate
A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The length of the prism is cm. Find the volume in cm³.
Explanation
. .
Q6·Moderate
A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The length of the prism is cm. Find the volume in cm³.
Explanation
. .
Q7·Moderate
A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The length of the prism is cm. Find the volume in cm³.
Explanation
. .
Q8·Moderate
A triangular prism has a triangular cross-section with base cm and perpendicular height cm. The length of the prism is cm. Find the volume in cm³.
Explanation
. .
Q9·Challenging
A rectangular prism has a volume of cm³, a length of cm and a width of cm. Find the height in cm.
Explanation
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Q10·Challenging
A rectangular prism has a volume of cm³, a length of cm and a width of cm. Find the height in cm.
Explanation
.
Q11·Challenging
A triangular prism has a volume of cm³. The triangular cross-section has a base of cm and a perpendicular height of cm. Find the length of the prism in cm.
Explanation
. .
Q12·Challenging
A triangular prism has a volume of cm³. The triangular cross-section has a base of cm and the prism has a length of cm. Find the perpendicular height of the triangle in cm.
Explanation
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