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1Key to Five

Key to FiveUnit 13: Volume and Measure

•Finding missing sides•Volume in terms of π•Volume of 3D shapes•Converting units•Area of circle•Parts of a circle

The PiXL Ladder to Success

Worked Solutions

Section A

Question 1

Write down the names of the labelled parts of the circles below.

a …………………… d ………………… f …………...…

b……………………. e ………………… g ……………

c……………………. h …………….

(Total 3 marks)

Question 2

Here is a list of words that are connected with circles. arc radius chord diameter circumference sector

Label the four boxes on this diagram, by choosing the correct word from the list.

1 ……………………………………..

2 ……………………………………..

3 ……………………………………..

4 ……………………………………..

(Total 4 marks)

2Key to Five

circumferencediameterradius sector segmenttangent

chord

arc

a, b , c ALL correct A1 d, e both correct A1 f,g,h ALL correct A1or ANY 4 parts labelled correct A1 or ANY 6 parts labelled correct A1

Arc A1

sector A1

radius A1

diameter A1

a

b

c

d

d

e

f

h g

3Key to Five

Question 3

A circle has a radius of 4 cm.

Write down the length of the diameter.

Answer .....………………8……………… cm(Total 1 mark)

Question 4.(a) A circular dinner plate has a radius of 13cm.

Calculate the area of the dinner plate, giving your answer to 2 decimal places. 132 × π (M1)

530.93 cm2 (A1)

(2)

(b) A clock has a diameter of 60cm.

Calculate the area of the wheel. Give your answer to 1 decimal place.60/2=30

302 × π (M1)

2827.4 cm2 (A1)

(2)

(Total 4 marks)

4Key to Five

Question 5.

Find the area of the semi-circle shown.

The diagram is not to scale and has a diameter of 20cm.

Give your answer to 2 decimal places.

20/2=10

102× π2

(M1, M1)

157.08 cm2 (A1)

(Total 3 marks)

Question 6.

Find the area of the shaded area shown.

Leave your answer in terms of π.

3cm

5cm

(2.5¿¿2 × π )−(1.52× π )¿ (M1)

6.25 π−2.25 π (A1)

4 π cm2 (A1)

(Total 3 marks)

5Key to Five

20

Question 7.A rectangular circuit board secures 12 wires in place. The wires are 4mm in diameter and the circuit board is 30mm by 10mm as shown on the diagram.Regulations state that not more than 40% of the area of the circuit board should be wire. Does this design meet the regulations?You must show all of your workings. Diagram NOT to scale

30mm

10mm

12 ×22× π=150.796 mm2 (M1 M1)30×10=300 mm2 (A1)

150.796 ÷ 300× 100=50.3 % (A1)

No ,the circuit board does not meet the regulations asis40

% (B1)

(5)

Question 8.The area of a 2p coin is 5.3 cm2.

How many 2p coins would be needed to be lined up to span a distance of 10m?

√5.3÷ π =1.3cm (M1 A1)

1.3 ×2=2.6 cm (M1)

1000 ÷ 2.6=384.6 (M1)

385 2 p coins are needed (A1)

6Key to Five

(Total 5 marks)

Question 9.(a) A circular dinner plate has a radius of 15cm.

Calculate the area of the dinner plate, giving your answer to 2 decimal places. 152 × π (M1)

705.86 cm2 (A1)

(2)

(b) A clock has a diameter of 20cm.

Calculate the area of the clock face. Give your answer to 1 decimal place.20/2=10

102 × π (M1)

314.2 cm2 (A1)

(2)

(Total 4 marks)

7Key to Five

Section B

Question 10

Change 7 m2 to cm2.

………70 000…………cm2

(Total 2 marks)

Question 11

The volume of a cube is 8 m3. (b) Change 8 m3 to cm3.

...............8 000 000........... cm3

(2)Question 12

The volume of a cylinder is 350cm3. Express the volume in mm3.

……350 000…………………… mm3

(1)

Question 13

The area of a classroom is 5m2. What is the area of the classroom in mm2 ?

…5 000 000……………………… mm2

(1)Question 14

A field has an area of 105m2. What is this in km2 ?

……0.000105…………………… km2

(1)

Question 15

Convert :

(a) 94,000 mm2 into cm2

. ...940...................... cm3

8Key to Five

(b) 0.08cm3 into mm3

………80………………… mm3

(2)

Section C

Question 16.Find the volumes of the following prisms:

(a)

6x8x10=480 cm3(M1 A1)………………………cm3

(2)(b)

½ x base x width x depth ½ x 6x8x4=96cm3 (M1 A1)

………………………cm3

(2)(c)

π r2h=volume (M1)

π× 4.22 ×5=277 cm3 (M1 A1)………………………m3

(3)(d)

½ (a+b)h x depth= volume (M1) ½ (6+2)x8 x7= 224cm3 (M1 A1)

………………………cm3

(3)

9Key to Five

Question 17.Find the volume of the trapezoidal prism when x is worth 5.

¿ sides=62∧22 (M1 for any correct substitution)

12

(62+22 )× 15 ×7=volume (M1)

volume=4410 (A1)………………………cubic units

(3)Question 18.This is a diagram of a cylindrical container with 1000ml of water in it.The radius of the container is 6cm. 1ml = 1cm3.What is the height of the water in the container?

π r2h=volumeπ × 62 ×?=1000100036 π

=8.84 cm

………………………cm(3)

Question 19.How many litres of water can be held in a swimming pool with the dimensions shown below?1 litre=1000cm3

½ x(2.5+1.2)x50x20=1850 m3

(M1 A1)1m3=1,000,000cm3

1850 x 1,000,000 = 1,850,000,000cm3 (M1)1,850,000,000/1000=1,850,000 litres (A1)

………………………litres

10Key to Five

6cm

(4)

(Total 10 marks)

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