True or False? A volume is measured in square units such as cm².

False. A volume is measured in cubic units such as cm³, because three lengths have been multiplied together. An answer written in cm² would be an area, and leaving the units off altogether is just as costly.

What should you check about the units before using a volume formula?

That every length going in is measured in the same unit. A solid given partly in metres and partly in centimetres has to be converted first, and the answer then comes out in the cube of whichever unit you chose.

How do you find the volume of a composite solid?

Split it into standard solids whose formulae you have, and work out each volume separately. Then add the volumes where solids are joined together, or subtract where one solid has been removed from another.

True or False? The volume of a block with a cylindrical hole drilled through it is the block's volume minus the cylinder's volume.

True. The hole is a standard solid that has been removed, so its volume is taken away from the volume of the block it was cut from. The hole still has to be measured as a cylinder in its own right, using its radius and the depth it is drilled to.

National 5MathsSQAApplications of MathematicsFlashcardsGeometric SkillsVolume

Volume (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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FrontVolume of Standard Solids
In the volume of a prism, $V = A h$ , what does $A$ stand for?

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Cards in this collection (11)

In the volume of a prism, $V = A h$ , what does $A$ stand for?
The area of the cross-section, the shape that stays the same all the way through the prism.
It is not simply whichever face is drawn at the front, so identify the constant cross-section first and find its area, then multiply by the length of the prism.
A squash ball has a diameter of 44 mm. What is its volume in cubic centimetres, to 1 decimal place?
The volume is 44.6 cm³.
Convert to centimetres first, so 44 mm is 4.4 cm, then halve it to get the radius of 2.2 cm.
Substituting into the given formula gives $\frac{4}{3} \times π \times 2 . 2^{3} = 44.60 . . .$
Complete the working for a cylinder of radius 3 cm and height 10 cm:
$V = π \times 3^{2} \times 10 =______π so V =______to 1 d.p.$
The completed working is:
$V = π \times 3^{2} \times 10 = 90 π so V = 282.7 to 1 d.p.$
The radius is squared but the height is not, which is the order the formula sets out.
True or False?
A volume is measured in square units such as cm².
False.
A volume is measured in cubic units such as cm³, because three lengths have been multiplied together.
An answer written in cm² would be an area, and leaving the units off altogether is just as costly.
How does the volume of a cone compare with that of a cylinder of the same base and height?
The cone is exactly one third of the cylinder.
The two given formulae are $V = π r^{2} h$ and $V = \frac{1}{3} π r^{2} h$ , which differ only by that factor.
Holding the two side by side is the easiest way to avoid picking the wrong one off the formula sheet.
What should you check about the units before using a volume formula?
That every length going in is measured in the same unit.
A solid given partly in metres and partly in centimetres has to be converted first, and the answer then comes out in the cube of whichever unit you chose.
How do you find the volume of a composite solid?
Split it into standard solids whose formulae you have, and work out each volume separately.
Then add the volumes where solids are joined together, or subtract where one solid has been removed from another.
Complete the method for a hemisphere:
A hemisphere is half a sphere, so work out the volume of the whole sphere using the given formula and then $______$ it by $______$ to finish.
The completed method is:
A hemisphere is half a sphere, so work out the volume of the whole sphere using the given formula and then divide it by 2 to finish.
The same approach works for any simple fraction of a standard solid: find the whole one first, then take the fraction you need.
A brick is a 5 cm cube with a cylinder on top, and the total height is 9 cm. How tall is the cylinder?
The cylinder is 4 cm tall.
The total height covers both parts, so the cube's height is taken off it: $9 - 5 = 4$ .
A dimension you need is often not given directly in a composite solid, and has to be recovered from the overall measurements first.
A brick is a 5 cm cube with a cylinder of diameter 5 cm and height 4 cm on top. What is its volume, to 3 significant figures?
The volume is 204 cm³.
The cube gives $5 \times 5 \times 5 = 125$ , and the cylinder has radius 2.5 cm, giving $π \times 2 . 5^{2} \times 4 = 78.54 . . .$
The two parts are joined, so the volumes are added: $125 + 78.54 = 203.5 . . .$
True or False?
The volume of a block with a cylindrical hole drilled through it is the block's volume minus the cylinder's volume.
True.
The hole is a standard solid that has been removed, so its volume is taken away from the volume of the block it was cut from.
The hole still has to be measured as a cylinder in its own right, using its radius and the depth it is drilled to.

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