P5P6 Volume of Partially Filled Tank with Unknown Height

Volumes of partially filled containers will require students to make use of the given values such as the available "Lengths", "Breadths". "Heights" and "Volumes" in order to calculate the required value that is not given.

Such questions are common in P5 and P6 exams in Paper 2.

Calculator usage is allowed.

A rectangular tank as the following dimensions.

Length : 30 cm

Breadth : 24 cm

This tank is filled with water up to a height of 48 cm.

The tank is ²/₇ filled with water.

a) How much water is needed to fill the tank?

b) What is the volume of the tank?

 

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P6 Math: Circle with a Square (2 identical isosceles triangles)

This is a circle question that also requires knowledge of triangles and squares.

The radius is not given but the area of the square or triangle is given.

Students will find it difficult to find the area of the circle due to the missing radius.

Such questions appear in Paper 2 of Prelim papers.

Calculator usage is allowed.

An oil drum cylinder has a circular base
but is a rectangle when viewed from the side

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P5/P6 Volume of Partially Filled Container with Unknown Height

A partially filled tank and its volume of water is given.

With the breadth and length, students must find out the missing "height" and "capacity" of the given tank.

Such questions are common in P5 and P6 exams in Paper 2.

Calculator usage is allowed.

A rectangular tank has a length of 20 cm and breadth of 16 cm.

The tank is ²/₅ filled with water.

There is now 7040 cm³ of water in the tank.

a) What is the height of the tank?

b) What is the volume of the tank?

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P5/P6 Volume of Partially Filled Container

Volume is a topic taught in P5 that addresses the 3-D space after students have comnpleted learning of 2-D shapes such as squares, rectangles and triangles.

Besides length and breadth, the height is what that gives a 2-D shapes another dimension.

Partially filled containers are often tested in Paper 2 of P5 and P6 exam papers.

Calculator usage is allowed.

A rectangular tank has the dimensions 55cm by 30cm by 40cm.

This tank is now ¹/₃ filled with water.

a) What is the volume of water is in the tank now?

b) What is the volume of water needed to fill the tank completely?

Partially filled water tanks

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P5/P6 Math: Triangle sharing Base and Height with Rectangle

The area of a triangle are actually expressed as half the area of a rectangle or square.

This above concept requires students to know that regardless of how the triangle looks like, it's area will be half of a rectangle that shares the same base and height as it shares the same length and breadth of a rectangle.

Such questions are common in Paper 1 of P5/P6 exams.

Calculator usage is not allowed.

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P5/P6 Math: Figure of 2 Overlapping Triangles

2 overlapping triangles sharing the same base but with different heights shares a common overlapped area.

Such questions requires students to know that the sum of the area of both triangles will definitely be more than the actual area of the figure shown.

Such questions are common in Paper 1 of P5/P6 exam papers.
Calculator usage is not allowed.

Triangular shaped support structures at the Eiffel Tower

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P6 Math: Overlapping Triangles (Advanced)

The question presents 2 overlapping triangles sharing the same base but with different heights.

Such questions requires students to understand the concept of "constant difference" on top of knowing how to calculate the basic area of triangle using the known formula.

Such questions may appear in Paper 2 of P6 exams.

Calculator usage is allowed.

More overlapping triangles questions here.

Triangles on roller coasters' structures provides strength in its support

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P6 Math: Area of Triangle in a Rectangle

A rectangle or square is presented with a triangle inside the shape.
The 3 corners of the triangle are touching the sides of the rectangle/square.

Such questions require students to use the concept that triangle is half of the area of the rectangle/square that it shares its base and height with.

These questions appear can appear in both Paper 1 and in Paper 2.

For the purposes of this practice,
calculator usage is allowed.

Triangular and other shaped dices

The figure below consists of a square with an area of 200 cm².

Triangle BDF has its 3 corners touching the sides of the square.

AB, AF, BC and EF have the same length as each other.

What is the area of triangle BDF?

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P5/P6 Math : Water in Partially-Filled Tanks to fill up Multiples of Smaller Containers

Such questions that deals with a large volume of water requires student to redistribute the water into smaller containers.

Both the dimensions of the larger tanks and smaller containers are given.
But the larger container is not filled to the brim.

Questions like these usually appear in Paper 2 of P5/P6 papers.
Calculator usage is allowed.

A large tank with dimensions of 32cm by 18cm by 12cm is ¹/₃ filled with water.

The water is used to fill smaller cubical containers with sides of 2cm.

How many of such smaller containers can be filled with the water from the large tank?

Glass filled with water to the brim

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P5/P6 Math: Volume: Water Transfers Between 2 Containers

This question which addresses the P5/P6 topic of Volume requires students to be able to find a common height of water after the volume of water is shared between 2 containers.

This can appear in P5 or P6 Paper 2 so calculator usage is acceptable.

How water is purified and made safe for consumption

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P5/P6 Math: Volume: Cutting Cubes from Cuboids

This question which addresses the P5 topic of Volume requires students to consider the cuboid as a solid, as opposed to an empty container.

Students are required to calculate the number of identical cubes that can be cut out from the given cuboid.

This can appear in P5 Paper 2 so calculator usage is acceptable.

Such questions also may appear in P6 Paper 1 where students are not allowed the usage of calculators.

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