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.

True or False? The surface area of a hemisphere comprises the surface area of a sphere and the area of a circle of the same radius .

False. The surface area of a hemisphere comprises half the surface area of a sphere, and the area of a circle of the same radius .

True or False? The surface area of a cuboid consists of three pairs of equal rectangles .

True. The surface area of a cuboid consists of three pairs of equal rectangles .

True or False? The net of a cylinder consists of two circles and a rectangle .

True. The net of a cylinder consists of two circles and a rectangle .

IGCSEMathsCambridge (CIE)CoreFlashcardsLengths, Areas & VolumesVolume & Surface Area

Volume & Surface Area (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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FrontVolume
What is the formula for the volume of a cuboid?
BackVolume
The formula for the volume of a cuboid is $V = l \times w \times h$
Where:
$V =$ volume
$l =$ length
$w =$ width
$h =$ height
BackVolume
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FrontVolume
What is the formula for the volume of a cylinder?
BackVolume
The formula for the volume of a cylinder is $V = π r^{2} h$
Where:
$V =$ volume
$r =$ radius
$h =$ height
FrontVolume
What is the formula for the volume of a cone?
BackVolume
The formula for the volume of a cone is $V = \frac{1}{3} π r^{2} h$
Where:
$V =$ volume
$r =$ radius
$h =$ perpendicular height

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Cards in this collection (17)

What is the formula for the volume of a cuboid?
The formula for the volume of a cuboid is $V = l \times w \times h$
Where:
- $V =$ volume
- $l =$ length
- $w =$ width
- $h =$ height
What is the formula for the volume of a cylinder?
The formula for the volume of a cylinder is $V = π r^{2} h$
Where:
- $V =$ volume
- $r =$ radius
- $h =$ height
What is the formula for the volume of a cone?
The formula for the volume of a cone is $V = \frac{1}{3} π r^{2} h$
Where:
- $V =$ volume
- $r =$ radius
- $h =$ perpendicular height
What is the formula for the volume of a sphere?
The formula for the volume of a sphere is $V = \frac{4}{3} π r^{3}$
Where:
- $V =$ volume
- $r =$ radius
What is the formula for the volume of a pyramid?
The formula for the volume of a pyramid is $V = \frac{1}{3} A h$
Where:
- $V =$ volume
- $A =$ area of the base
- $h =$ perpendicular height of the pyramid
What is the formula for the volume of a prism?
The formula for the volume of a prism is $V = A l$
Where:
- $V =$ volume
- $A =$ cross-sectional area
- $l =$ length
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 $38$ cm² 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 $^{3}$ .
What is the formula for the surface area of a cylinder?
The formula for the surface area of a cylinder is $A = 2 π r^{2} + 2 π r h$
Where:
- $A =$ surface area
- $r =$ radius
- $h =$ height
True or False?
The formula for the curved surface area of a cone is $A = π r l + π r^{2}$
Where:
- $A =$ surface area
- $r =$ radius
- $l =$ slant height
False.
$A = π r l + π r^{2}$ is the total surface area of a cone.
The formula for the curved surface area of a cone is $A = π r l$
Where:
- $A =$ surface area
- $r =$ radius
- $l =$ slant height
( $π r^{2}$ is the area of the circular base of the cone.)
What is the formula for the surface area of a sphere?
The formula for the surface area of a sphere is $A = 4 π r^{2}$
Where:
- $A =$ surface area
- $r =$ radius
True or False?
The surface area of a hemisphere comprises the surface area of a sphere and the area of a circle of the same radius.
False.
The surface area of a hemisphere comprises half the surface area of a sphere, and the area of a circle of the same radius.
True or False?
The surface area of a cuboid consists of three pairs of equal rectangles.
True.
The surface area of a cuboid consists of three pairs of equal rectangles.
What is the formula for the total surface area of a cone?
The formula for the total surface area of a cone is $A = π r^{2} + π r l$
Where:
- $A =$ surface area
- $r =$ radius
- $l =$ slant height
True or False?
The net of a cylinder consists of two circles and a rectangle.
True.
The net of a cylinder consists of two circles and a rectangle.

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