Volume of cylinders
Calculate the volume of a cylinder using , given the radius or diameter, and find the height when the volume is known.
Worked examples
Finding the volume of a cylinder given radius and height
Straightforward
Problem
Find the volume of a cylinder with radius cm and height cm. Give your answer correct to 2 decimal places.
1
Write the formula for the volume of a cylinder.
2
Substitute and .
3
Calculate to 2 decimal places.
cm³
Answer
cm³
Finding the height of a cylinder given its volume and diameter
Moderate
Problem
A cylinder has a diameter of cm and a volume of cm³. Find the height of the cylinder.
1
Find the radius from the diameter.
cm
2
Write the formula and substitute the known values.
3
Solve for .
cm
Answer
cm
Volume of a hollow cylinder
Challenging
Problem
A hollow cylindrical pipe has an outer radius of cm, an inner radius of cm, and a length of cm. Find the volume of material in the pipe correct to 2 decimal places.
1
Find the volume of the outer (solid) cylinder.
2
Find the volume of the inner (hollow) cylinder.
3
Subtract to find the volume of material.
4
Calculate to 2 decimal places.
cm³
Answer
cm³
Practise
Q1·Straightforward
Find the volume of a cylinder with radius cm and height cm. Give your answer correct to 2 decimal places.
Explanation
cm³
Q2·Straightforward
Find the volume of a cylinder with radius m and height m. Give your answer correct to 2 decimal places.
Explanation
m³
Q3·Straightforward
A cylinder has radius cm and height cm. Find its volume correct to 2 decimal places.
Explanation
cm³
Q4·Straightforward
Find the volume of a cylinder with radius cm and height cm. Give your answer correct to 2 decimal places.
Explanation
cm³
Q5·Moderate
A cylinder has a diameter of cm and a height of cm. Find its volume correct to 2 decimal places.
Explanation
cm; cm³
Q6·Moderate
A cylinder has a diameter of m and a height of m. Find its volume correct to 2 decimal places.
Explanation
m; m³
Q7·Moderate
A cylinder has radius cm and volume cm³. Find its height (in cm).
Explanation
cm
Q8·Moderate
A cylinder has radius cm and volume cm³. Find its height (in cm).
Explanation
cm
Q9·Challenging
Cylinder A has radius cm and height cm. Cylinder B has radius cm and height cm. Find the difference in their volumes, correct to 2 decimal places.
Explanation
cm³; cm³; Difference cm³
Q10·Challenging
A hollow cylinder has an outer radius of cm, an inner radius of cm, and a height of cm. Find the volume of material in the cylinder correct to 2 decimal places.
Explanation
; ; cm³
Q11·Challenging
A cylindrical water tank has radius cm and height cm. How many litres of water does it hold when full? Give your answer correct to 2 decimal places. ( litre cm³)
Explanation
cm³; litres
Q12·Challenging
A hollow cylindrical pipe has an outer diameter of cm, an inner diameter of cm, and a length of cm. Find the volume of material in the pipe correct to 2 decimal places.
Explanation
Outer cm, inner cm; cm³