# 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.

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__Volume Involving a Common Height Question 1__

__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 cm^{2}

Base area of Tank Y = 94 cm × 80 cm = 7520 cm^{2}

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 cm^{3}

4320 u = 64 800 cm^{3}

1u = 64 800 ÷ 4320

= 15 cm (Ans)

__Volume Involving a Common Height Question____ 2__

__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 cm^{2}

Base area of Tank Q = 72 cm x 24 cm = 1728 cm^{2}

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 cm^{3}

3228 u = 90 384 cm^{3}

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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To Your Child’s Success,

Ms Nelly Ke

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

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