Practise
Papers
Your area
Past papers
Get ready
Learn and practise
One table
Year 4 check
Spelling lists
More English
Home / Practice / Maths
Cuboids, missing dimensions, and litres poured into millilitres.
Question 1 of 12
A box has a volume of 125 cm³. Its base measures 5 cm by 5 cm. How tall is the box?
The base area is 5 × 5 = 25 cm². Volume is base area × height, so the height is volume ÷ base area: 125 ÷ 25 = 5 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 5 × 5 × 5 = 125 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
The answer is C. The base area is 5 × 5 = 25 cm². Volume is base area × height, so the height is volume ÷ base area: 125 ÷ 25 = 5 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 5 × 5 × 5 = 125 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
A jug holds 5 litres 200 ml of squash. It is poured into glasses holding 200 ml each. How many full glasses can be filled?
Put everything into the same unit first. 5 litres is 5,000 ml, so the jug holds 5,000 + 200 = 5,200 ml. 5,200 ÷ 200 = 26 remainder 0, so 26 glasses can be filled completely and 0 ml is left in the jug — not enough for another. 1 litre is 1,000 ml. It is the conversion that comes up most often of all.
The answer is A. Put everything into the same unit first. 5 litres is 5,000 ml, so the jug holds 5,000 + 200 = 5,200 ml. 5,200 ÷ 200 = 26 remainder 0, so 26 glasses can be filled completely and 0 ml is left in the jug — not enough for another. 1 litre is 1,000 ml. It is the conversion that comes up most often of all.
A cuboid measures 7 cm by 7 cm by 2 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 7 × 7 = 49, then 49 × 2 = 98 cm³. The units are cm³ because three lengths have been multiplied. 49 cm² would be the area of one face, and 154 cm² would be the surface area — both different questions. Multiply two of the dimensions first, then the third. Doing all three at once invites arithmetic slips.
The answer is A. Volume is length × width × height, all three multiplied together: 7 × 7 = 49, then 49 × 2 = 98 cm³. The units are cm³ because three lengths have been multiplied. 49 cm² would be the area of one face, and 154 cm² would be the surface area — both different questions. Multiply two of the dimensions first, then the third. Doing all three at once invites arithmetic slips.
A box has a volume of 336 cm³. Its base measures 7 cm by 6 cm. How tall is the box?
The base area is 7 × 6 = 42 cm². Volume is base area × height, so the height is volume ÷ base area: 336 ÷ 42 = 8 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 7 × 6 × 8 = 336 cm³. Volume divided by area gives a length. The units confirm it: cm³ ÷ cm² = cm.
The answer is D. The base area is 7 × 6 = 42 cm². Volume is base area × height, so the height is volume ÷ base area: 336 ÷ 42 = 8 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 7 × 6 × 8 = 336 cm³. Volume divided by area gives a length. The units confirm it: cm³ ÷ cm² = cm.
A box has a volume of 616 cm³. Its base measures 11 cm by 8 cm. How tall is the box?
The base area is 11 × 8 = 88 cm². Volume is base area × height, so the height is volume ÷ base area: 616 ÷ 88 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 11 × 8 × 7 = 616 cm³. Multiply back to check, every time.
The answer is A. The base area is 11 × 8 = 88 cm². Volume is base area × height, so the height is volume ÷ base area: 616 ÷ 88 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 11 × 8 × 7 = 616 cm³. Multiply back to check, every time.
A jug holds 9 litres 450 ml of squash. It is poured into glasses holding 250 ml each. How many full glasses can be filled?
Put everything into the same unit first. 9 litres is 9,000 ml, so the jug holds 9,000 + 450 = 9,450 ml. 9,450 ÷ 250 = 37 remainder 200, so 37 glasses can be filled completely and 200 ml is left in the jug — not enough for another. Convert to the smaller unit before dividing. Mixing litres and millilitres in one calculation never ends well.
The answer is C. Put everything into the same unit first. 9 litres is 9,000 ml, so the jug holds 9,000 + 450 = 9,450 ml. 9,450 ÷ 250 = 37 remainder 200, so 37 glasses can be filled completely and 200 ml is left in the jug — not enough for another. Convert to the smaller unit before dividing. Mixing litres and millilitres in one calculation never ends well.
A jug holds 9 litres 350 ml of squash. It is poured into glasses holding 300 ml each. How many full glasses can be filled?
Put everything into the same unit first. 9 litres is 9,000 ml, so the jug holds 9,000 + 350 = 9,350 ml. 9,350 ÷ 300 = 31 remainder 50, so 31 glasses can be filled completely and 50 ml is left in the jug — not enough for another. "Full glasses" means the remainder is left behind. Round down, not up.
The answer is C. Put everything into the same unit first. 9 litres is 9,000 ml, so the jug holds 9,000 + 350 = 9,350 ml. 9,350 ÷ 300 = 31 remainder 50, so 31 glasses can be filled completely and 50 ml is left in the jug — not enough for another. "Full glasses" means the remainder is left behind. Round down, not up.
A cuboid measures 10 cm by 4 cm by 3 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 10 × 4 = 40, then 40 × 3 = 120 cm³. The units are cm³ because three lengths have been multiplied. 40 cm² would be the area of one face, and 164 cm² would be the surface area — both different questions. Count the units: cm for length, cm² for area, cm³ for volume. The little number tells you how many lengths were multiplied.
The answer is A. Volume is length × width × height, all three multiplied together: 10 × 4 = 40, then 40 × 3 = 120 cm³. The units are cm³ because three lengths have been multiplied. 40 cm² would be the area of one face, and 164 cm² would be the surface area — both different questions. Count the units: cm for length, cm² for area, cm³ for volume. The little number tells you how many lengths were multiplied.
A cuboid measures 7 cm by 5 cm by 4 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 7 × 5 = 35, then 35 × 4 = 140 cm³. The units are cm³ because three lengths have been multiplied. 35 cm² would be the area of one face, and 166 cm² would be the surface area — both different questions. Count the units: cm for length, cm² for area, cm³ for volume. The little number tells you how many lengths were multiplied.
The answer is B. Volume is length × width × height, all three multiplied together: 7 × 5 = 35, then 35 × 4 = 140 cm³. The units are cm³ because three lengths have been multiplied. 35 cm² would be the area of one face, and 166 cm² would be the surface area — both different questions. Count the units: cm for length, cm² for area, cm³ for volume. The little number tells you how many lengths were multiplied.
A box has a volume of 224 cm³. Its base measures 4 cm by 8 cm. How tall is the box?
The base area is 4 × 8 = 32 cm². Volume is base area × height, so the height is volume ÷ base area: 224 ÷ 32 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 8 × 7 = 224 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
The answer is B. The base area is 4 × 8 = 32 cm². Volume is base area × height, so the height is volume ÷ base area: 224 ÷ 32 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 8 × 7 = 224 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
A box has a volume of 560 cm³. Its base measures 10 cm by 8 cm. How tall is the box?
The base area is 10 × 8 = 80 cm². Volume is base area × height, so the height is volume ÷ base area: 560 ÷ 80 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 10 × 8 × 7 = 560 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
The answer is D. The base area is 10 × 8 = 80 cm². Volume is base area × height, so the height is volume ÷ base area: 560 ÷ 80 = 7 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 10 × 8 × 7 = 560 cm³. Work out the base area first. It turns a three-number problem into a two-number one.
A cuboid measures 13 cm by 4 cm by 3 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 13 × 4 = 52, then 52 × 3 = 156 cm³. The units are cm³ because three lengths have been multiplied. 52 cm² would be the area of one face, and 206 cm² would be the surface area — both different questions. The order does not matter. Pick the two that multiply most easily.
The answer is D. Volume is length × width × height, all three multiplied together: 13 × 4 = 52, then 52 × 3 = 156 cm³. The units are cm³ because three lengths have been multiplied. 52 cm² would be the area of one face, and 206 cm² would be the surface area — both different questions. The order does not matter. Pick the two that multiply most easily.
Keep a record of how this went? It stays in this browser only and is never sent to us. You can clear it any time.
Saved to your record on this device. See the record
Try another set Pick a different topic
More shape and space first, then the rest of maths.
Every maths topic · A timed maths mock paper
For grown-ups: message us
A question, an idea, or something that isn't working? We read every message.
Please don't include a child's name or school.
Saved and sent to our inbox. Privacy
Thank you
Your message has reached us.