Saturday X-tra
X-Sheet: 13
Revision of Grade 12 Space and Shape Part 2
3D Shapes
Key Concepts
In this session we will focus on summarising what you need to know about:
- Measurements of capacity and volume
- Volume of prisms
Terminology & definitions
- Capacity – is the volume of a 3D container or shape
- Volume – is a measure of the amount that can be held or contained by
something (container).
- Capacity or volume is measured in units CUBED, e.g. cm3 or m3.
The capacity of fluids can be measured in millilitres, litres or kilolitres.
Conversions to know:
- 1cm3 = 1000mm3
- 1cm3 = 1ml
10mm
1cm
3
1cm
1cm
=
1000mm3
1cm
10mm
10mm
- 1000cm3 = 1000ml = 1 litre
- 1m3 = 1 000 000cm3 = 1000 litres = 1 kilolitre
- 1km3 = 1 000 000 000m3
- Volume of a prism = area of cross section x length of prism
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Common volumes of prisms:
- Volume of a rectangular prism = length x breadth x height
length
height
breadt
h
- Volume of a cylinder = area circle x height = ‫ ݎߨ = ܣ‬ଶ h
‫ ݎߨ = ܣ‬ଶ
Height / length
- Volume of triangular prism = area of triangle x length
= ½ base x ┴ height of triangle x length
Area triangle =
½ base x ┴ height
length
Concept:
Measurement of Capacity and Volume
X-ample 1:
0.11 cm3 = _____ mm3
X-ample 2:
150 ml = ______ cm3
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X-ample 3:
352 m3 = ___________l = ___________ kl
X-ample 4:
123 kl = ____________m3
Concept:
Volumes of prisms
X-ample 5:
Thomas buys a small fish tank from "Fish World" for R199,99.
The dimensions of the fish tank are 91 cm by 32 cm by 35 cm.
35 cm
32 cm
91 cm
1. a. Calculate the volume of the tank in cm3.
b. Convert the volume of the tank into m3.
2. How many litres of water will the tank hold when full?
1000 cm3 = 1 litre
X-ample 6:
Lebo purchased a cylindrical water container to store her treated drinking water. The
height of the container is 60 cm and the radius is 20 cm, as shown below.
Calculate the volume of the water container.
Use the formula: Volume of cylinder = π x (radius)2 x height using π= 3,14.
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X-ample 7:
This is a diagram of the cross section of a swimming pool.
1
2
3
Calculate the volume of the whole pool.
If the pool is only 95% filled how much water is needed? 1m3 = 1kl
If the pool is filled at a rate of 500 litres per hour – how long will it take to fill
the tank?
Area of a trapezium = ½ (length of top + length of bottom) x ┴ height of trapezium
Volume of a prism = area of cross section x length
X-ample 8:
Each small equilateral triangular Toblerone box has the following dimensions:
5 cm
20cm
Find the volume of the box. Give your answer to 1 decimal place.
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X-ample 9:
Ronwyn and Bronwyn are twins. They plan to celebrate their 21st birthday by having
a big party. Ronwyn has decided that she wants a round cake, while Bronwyn has
decided to have a ring cake, as shown in the pictures below.
The dimensions of each cylindrical cake are as follows:
The following formulae (using π = 3,14) may be used:
2
Volume of a cylinder = π×(radius) × height
2
2
Volume of a cylindrical ring = π × (R – r ) × height
where R = outer radius and r = inner radius
Using the volume of each cake, determine which of the two cakes is better value for
money if the costs of the two cakes are the same.
Give a reason for your answer, showing ALL your calculations.
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X-ample 10:
Ben wants to work out the volume of a can of beans. According to his
measurements, the can measures 74mm from one side of the top to the other
(diameter). The can is also 109 mm high. Find the volume of the tin.
ࢂ࢕࢒࢛࢓ࢋ = ࣊࢘૛ ‫ܐ‬
X-ample 11:
Find the volume of the rectangular prism, in kilolitres.
Volume of a rectangular prism = length x breadth x height
10m
5m
2m
X-ercise
1.
Find the volume of the triangular prism. Give your answer to 1 d.p.
6 cm
10cm
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2.
A circular pool above the ground has a diameter of 7,5 m and a height of 2 m.
3.
Calculate the volume (in m3) of the pool.
Give your answer rounded off to one decimal place.
Cailin's LCD TV screen is a new slim model that is only 39,7 mm thick. The
rectangular screen is 45 cm high and 60 cm wide. The TV stands on a round
base with a diameter of 20 cm that is 2 cm thick and is held up by a swivel that
is 5 cm high, as shown in the diagram below.
Determine the volume (in cm3) of the rectangular box that the TV will be delivered
in if there is an allowance of 2 cm (on both sides) for all measurements to
package the TV, as shown in the side view above.
Given the formula:
Volume =
length x breadth x height
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X-ercise Answers.
1.
┴ height
= 5,196152423cm
Volume = area triangle x length = ½(6 x 5,196…) x 10 = 155,9cm3
2. Volume = ‫ ח‬r2 h (‫ = ח‬3,14 ; r = 3,75m ; h = 2)
Volume = 3,14 x (3,75)2 x 2 = 88,3125 ≈ 88,3 m3 (1 d.p)
3. Total height of the TV = 45 + 5 + 2 = 52cm
Total breadth of the TV = 20 cm
Total length of the TV = 60cm
Add 2cm on either side of the height, breadth and length (+ 4 cm)
Dimensions of the box:
Height = 52 + 4 = 56cm
Breadth = 20 + 4 = 24cm
Length = 60 + 4 = 64cm
Volume of the BOX = 56 x 24 x 64 = 86 016cm3
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