Define the volume of a 3D shape.

Volume is a measure of how much space a 3D shape takes up. It is worked out from lengths in three dimensions, which is why every volume formula multiplies three lengths together.

You know a prism's volume and its length. How do you find the area of its cross-section?

Divide the volume by the length. Since the volume is the cross-sectional area multiplied by the length, dividing undoes that and recovers the area.

A solid in a problem is not a simple cuboid. What is worth checking before anything else?

Whether it is a prism , meaning the same cross-section runs all the way through it. If it is, the volume is the area of that cross-section multiplied by the length, however awkward the cross-section looks.

True or False? The cross-section of a prism has to be a simple shape such as a rectangle or a triangle.

False. The cross-section can be any shape at all, including an L-shape or another compound shape. What makes a solid a prism is that the cross-section stays the same all the way through, not that it is simple.

A prism has an L-shaped cross-section. How do you find its volume?

Find the area of the L-shaped cross-section first, then multiply that area by the length of the prism. The whole of the 2D area has to be worked out before the length is brought in at all.

Define the surface area of a 3D shape.

Surface area is the total of the areas of all the surfaces that make up the solid. It is a 2D idea applied to a 3D object, so it is measured in square units rather than cubic ones.

How do you find the surface area of a cuboid ?

Work out the area of each face and add them all together. A cuboid's opposite faces are identical, so there are only three different areas to find, each of which is then counted twice.

True or False? Every cylinder in a surface-area question has two circular ends to include.

False. An open cylinder such as a tube or an open-topped tank has one end or none at all. Work out from the solid described how many of its surfaces actually exist before adding them up.

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Volume & Surface Area (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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Define the volume of a 3D shape.

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Define the volume of a 3D shape.
Volume is a measure of how much space a 3D shape takes up.
It is worked out from lengths in three dimensions, which is why every volume formula multiplies three lengths together.
What is the formula for the volume of a cuboid?
$V = l w h$ , the length multiplied by the width multiplied by the height.
Some questions use the words depth or breadth instead of height or width, but the calculation is the same.
What is the formula for the volume of a prism?
$V = A l$ , the area of the cross-section multiplied by the length.
The cross-section can be any shape at all, so this one formula covers every prism.
You know a prism's volume and its length. How do you find the area of its cross-section?
Divide the volume by the length.
Since the volume is the cross-sectional area multiplied by the length, dividing undoes that and recovers the area.
True or False?
The volume of a cylinder can be found using the formula for the volume of a prism.
True.
A cylinder has the same cross-section all the way through, and that cross-section is a circle of area $π r^{2}$ .
Multiplying by the height gives $V = π r^{2} h$ , which is the prism formula with a circle in it.
A cylinder has radius $8$ cm and height $20$ cm. Complete the substitution:
$V = π \times______^{2} \times______$
The completed substitution is:
$V = π \times 8^{2} \times 20$
It is the radius that is squared, not the height, and this comes to $4020$ cm $^{3}$ to 3 significant figures.
A solid in a problem is not a simple cuboid. What is worth checking before anything else?
Whether it is a prism, meaning the same cross-section runs all the way through it.
If it is, the volume is the area of that cross-section multiplied by the length, however awkward the cross-section looks.
True or False?
The cross-section of a prism has to be a simple shape such as a rectangle or a triangle.
False.
The cross-section can be any shape at all, including an L-shape or another compound shape.
What makes a solid a prism is that the cross-section stays the same all the way through, not that it is simple.
A prism has an L-shaped cross-section. How do you find its volume?
Find the area of the L-shaped cross-section first, then multiply that area by the length of the prism.
The whole of the 2D area has to be worked out before the length is brought in at all.
An L-shaped prism has a cross-sectional area of $38$ cm $^{2}$ and a length of $10$ cm. Complete the working:
$V =______\times______=______$
The completed working is:
$V = 38 \times 10 = 380$
The volume is $380$ cm $^{3}$ .
Define the surface area of a 3D shape.
Surface area is the total of the areas of all the surfaces that make up the solid.
It is a 2D idea applied to a 3D object, so it is measured in square units rather than cubic ones.
How do you find the surface area of a cuboid?
Work out the area of each face and add them all together.
A cuboid's opposite faces are identical, so there are only three different areas to find, each of which is then counted twice.
A cuboid measures $2$ cm by $10$ cm by $15$ cm, and its three different faces have areas of $20$ , $30$ and $______$ cm $^{2}$ . Complete the total:
surface area $=______$ cm $^{2}$
The completed values are $150$ cm $^{2}$ for the third face and $400$ cm $^{2}$ in total.
The third face is $10 \times 15$ , and doubling each of $20$ , $30$ and $150$ gives $40 + 60 + 300 = 400$ .
What is the curved surface area of a cylinder?
$A = 2 π r h$ .
This is the circumference of the circular end multiplied by the height of the cylinder.
What is the total surface area of a closed cylinder?
$A = 2 π r h + 2 π r^{2}$ .
It is the curved surface plus the two circular ends, each of which has area $π r^{2}$ .
True or False?
Every cylinder in a surface-area question has two circular ends to include.
False.
An open cylinder such as a tube or an open-topped tank has one end or none at all.
Work out from the solid described how many of its surfaces actually exist before adding them up.

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