15.1- Introduction
• Solve problems involving:
(a) the perimeter and area of a rectangle and triangle
(b) the perimeter and area of a parallelogram and a trapezium
(c) the circumference and area of a circle
(d) arc length and sector area as fractions of the circumference
and area of a circle
(e) the surface area and volume of a cuboid, cylinder, prism,
sphere, pyramid and cone
(f) the areas and volumes of compound shapes
Formulae will be given for the surface area and volume of the sphere,
pyramid and cone.
Question 1 : The pentagon ABCDE is made from a square of side 12 cm and an isosceles triangle. The angle (ABC) ̂=135°
Calculate the perimeter of the pentagon?
15.2- 3D shapes
3D shapes are solids that consist of 3 dimensions, namely – length, breadth, and height. 3D in the word 3D shapes means three-dimensional. Every 3D geometric shape occupies some space based on its dimensions and we can see so many 3D shapes all around us in our day-to-day life. Some examples of 3D shapes are cube, cuboid, cone, and cylinder.
15.3- Volume of a prism
Question 1 : The 3.8 m3of concrete is made into the shape of a cylinder. The base has radius 0.5 metres.(a) Calculate the height of the cylinder? (b) The density of the concrete is 2400 kgm-3 Calculate the mass of the concrete?
15.4- Volume and surface area
If r is the radius of the sphere or cone,
l is the slant height of a cone
and h is the perpendicular height of a cone:
Curved surface area of a cone = πrl
Surface area of a sphere = 4πr2
Volume of a sphere =\(\frac{4}{3}\) πr3
Volume of a cone =\(\frac{1}{3}\) πr2 h
15.5- Assessment 15
Question 1 : Evelyn thinks she can save water by showering instead of bathing. Her shower uses 10.8 litres per minute and lasts 8 minutes. Eva assumes the water in her bath is in the shape of a cuboid 110cm x 50cm x 35cm. How many litres of water does she save?
Question 2 : A large rectangle is made by joining three identical small rectangles as shown
The perimeter of one small rectangle is 15 cm. Calculate the perimeter of the large rectangle ?
Question 3 : Convert 15 cm3 to mm3 ?
Question 4 : A pattern is made using 20 straight lines and 16 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line : cost of one arc = 2 : 3
Calculate the total cost of the metal in the pattern?
Question 5 : A tank is a cuboid measuring 50 cm by 35 cm by 20 cm
A container has a capacity of exactly 34 litres.
1 litre = 1000 cm3
Which has the greater capacity? A tank is a cuboid measuring 50 cm by 35 cm by 20 cm. All lengths are to the nearest centimetre. A container has a capacity of exactly 34 litres.
1 litre = 1000 cm3
Which has the greater capacity the tank or the container?
Question 6 : Solids X and Y are similar. X has volume 64 cm3 Y has volume 343 cm3: The surface area of X is 176 cm2. Calculate the surface area of Y ?
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15.6- Lifeskills 3 : Getting ready
Question 1 : The volume of a swimming ring, V cm3 , is given by
V=0.25π(b3-a2)
Calculate the volume when a=20 and b=30 ?
Question 2 : What is the size of an exterior angle of a regular decagon?