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Cuboids, missing dimensions, and litres poured into millilitres.
Question 1 of 12
A jug holds 3 litres 350 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. 3 litres is 3,000 ml, so the jug holds 3,000 + 350 = 3,350 ml. 3,350 ÷ 250 = 13 remainder 100, so 13 glasses can be filled completely and 100 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. 3 litres is 3,000 ml, so the jug holds 3,000 + 350 = 3,350 ml. 3,350 ÷ 250 = 13 remainder 100, so 13 glasses can be filled completely and 100 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 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 box has a volume of 96 cm³. Its base measures 4 cm by 4 cm. How tall is the box?
The base area is 4 × 4 = 16 cm². Volume is base area × height, so the height is volume ÷ base area: 96 ÷ 16 = 6 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 4 × 6 = 96 cm³. Volume divided by area gives a length. The units confirm it: cm³ ÷ cm² = cm.
The answer is D. The base area is 4 × 4 = 16 cm². Volume is base area × height, so the height is volume ÷ base area: 96 ÷ 16 = 6 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 4 × 6 = 96 cm³. Volume divided by area gives a length. The units confirm it: cm³ ÷ cm² = cm.
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 5 litres 350 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 + 350 = 5,350 ml. 5,350 ÷ 200 = 26 remainder 150, so 26 glasses can be filled completely and 150 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. 5 litres is 5,000 ml, so the jug holds 5,000 + 350 = 5,350 ml. 5,350 ÷ 200 = 26 remainder 150, so 26 glasses can be filled completely and 150 ml is left in the jug — not enough for another. "Full glasses" means the remainder is left behind. Round down, not up.
A box has a volume of 224 cm³. Its base measures 4 cm by 7 cm. How tall is the box?
The base area is 4 × 7 = 28 cm². Volume is base area × height, so the height is volume ÷ base area: 224 ÷ 28 = 8 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 7 × 8 = 224 cm³. Multiply back to check, every time.
The answer is B. The base area is 4 × 7 = 28 cm². Volume is base area × height, so the height is volume ÷ base area: 224 ÷ 28 = 8 cm. Doing it in two steps — base first, then divide — is safer than trying to divide by both numbers at once. Checking forwards: 4 × 7 × 8 = 224 cm³. Multiply back to check, every time.
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 11 cm by 2 cm by 7 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 11 × 2 = 22, then 22 × 7 = 154 cm³. The units are cm³ because three lengths have been multiplied. 22 cm² would be the area of one face, and 226 cm² would be the surface area — both different questions. The order does not matter. Pick the two that multiply most easily.
The answer is B. Volume is length × width × height, all three multiplied together: 11 × 2 = 22, then 22 × 7 = 154 cm³. The units are cm³ because three lengths have been multiplied. 22 cm² would be the area of one face, and 226 cm² would be the surface area — both different questions. The order does not matter. Pick the two that multiply most easily.
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.
A cuboid measures 7 cm by 7 cm by 5 cm. What is its volume?
Volume is length × width × height, all three multiplied together: 7 × 7 = 49, then 49 × 5 = 245 cm³. The units are cm³ because three lengths have been multiplied. 49 cm² would be the area of one face, and 238 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 C. Volume is length × width × height, all three multiplied together: 7 × 7 = 49, then 49 × 5 = 245 cm³. The units are cm³ because three lengths have been multiplied. 49 cm² would be the area of one face, and 238 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.
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