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.

This will be delivered to your email inbox.

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.

This will be delivered to your email inbox.

To Your Child’s Success,

Nelly Ke Math Tutor Grade Solution

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

Does your child need help in his or her studies?

1) Live Zoom Lessons at Grade Solution Learning Centre

At Grade Solution Learning Centre, we are a team of dedicated educators whose mission is to guide your child to academic success.  Here are the services we provide:

– Live Zoom lessons

– EdaptIQ™, a smart learning platform that tracks your child’s progress, strengths and weaknesses through personalised digital worksheets.

– 24/7 Homework Helper Service

We provide all these services above at a very affordable monthly fee to allow as many students as possible to access such learning opportunities.

We specialise in English, Math, and Science subjects.

You can see our fees and schedules here >>

Primary Math Tuition

Secondary Math Tuition

2) Pre-recorded Online courses on Jimmymaths.com

 

If you are looking for something that fits your budget, or prefer your child learn at his or her own pace, you can join our pre-recorded online Math courses.

Your child can:

– Learn from recorded videos

– Get access to lots of common exam questions to ensure sufficient practice

– Get unlimited support and homework help

You can see the available courses here >>

Math Online Courses