# Challenging Volume Questions (Involving a Common Height)

The main aim of this math revision note is to help your child become better at solving challenging PSLE Math volume question that involves a common height.

These type of volume questions involving a common height will assess your child’s understanding of three-dimensional shapes and his/her ability to form equations using what is given to solve for what is required.

Before you read on, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

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## Volume Involving a Common Height Question 1

Tank X and Tank Y are filled with water. Tank X is 64 cm long and 50 cm wide while Tank Y is 94 cm long and 80 cm wide. Both of them contain water and the height of water for both tanks is the same. Tank Y contains 64.8 litres more water than Tank X.

What is the height of the water in the tanks?

Solutions

Base area of Tank X = 64 cm × 50 cm = 3200 cm2

Base area of Tank Y = 94 cm × 80 cm = 7520 cm2

Since the height of water is the same, we can treat the height as 1u.

Recall: Volume = Base Area × Height

Volume of water in Tank X = 3200 × 1u = 3200 u

Volume of water in Tank Y = 7520 × 1u = 7520 u

Difference in volume = 7520 u – 3200 u = 4320 u

64.8 litres = 64 800 cm3

4320 u =  64 800 cm3

1u = 64 800 ÷ 4320

= 15 cm (Ans)

## Volume Involving a Common Height Question 2

Tank P and Tank Q are filled with water. Tank P is 50 cm long and 30 cm wide while Tank Q is 72 cm long and 24 cm wide. Both of them contain water and the height of water for both tanks is the same. Both tanks contain a total volume of 90.384 litres.

What is the height of the water in the tanks?

Solutions

Base area of Tank P = 30 cm x 50 cm = 1500 cm2

Base area of Tank Q = 72 cm x 24 cm = 1728 cm2

Since the height of water is the same, we can treat the height as 1u.

Recall: Volume = Base Area × Height

Volume of water in Tank P = 1500 × 1u = 1500 u

Volume of water in Tank Q = 1728 × 1u = 1728 u

Total volume = 1500 u + 1728 u = 3228 u

90.384 litres  = 90 384 cm3

3228 u = 90 384 cm3

1u = 90 384 ÷ 3228

= 28 cm (Ans)

Test your child’s understanding by taking this short quiz!

Click the button below.

Before you go, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

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Ms Nelly Ke
Math Specialist
Jimmy Maths and Grade Solution Learning Centre

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