**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 m^{3}of 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 = 4πr^{2}

Volume of a sphere =\(\frac{4}{3}\) πr^{3}

Volume of a cone =\(\frac{1}{3}\) πr^{2} 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 cm^{3} to mm^{3} ?

**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 cm^{3}

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 cm^{3}

Which has the greater capacity the tank or the container?

**Question 6 :** Solids X and Y are similar. X has volume 64 cm^{3 }Y has volume 343 cm3: The surface area of X is 176 cm^{2}. 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 cm^{3} , is given by

V=0.25π(b^{3}-a^{2})

Calculate the volume when a=20 and b=30 ?

**Question 2 :** What is the size of an exterior angle of a regular decagon?