Volume + surface area

Question 1

Equation for the volume of a Prism ?

Answer 1

Volume of prism = cross sectional area x length

Question 2

What is the unit for volume?

Answer 2

M^3

Question 3

Triangular face prism. Bace of face is 5cm, vertical height is 6cm. Length is 8cm. Give the volume.

Answer 3

V = 6x5/2 x 8 = 120cm^3

Question 4

Cylinder has a horizontal base length of 10cm, height of 5cm. Give the volume.

Answer 4

V = r^2 pi x 6
=5^2 pi x 6
= 471.2cm^3

Question 5

1000ml = ? Litre

Answer 5

1 litre

Question 6

1 ml = ? Cm^3

Answer 6

1 cm ^3

Question 7

What is surface area?

Answer 7

The area of the faces of the shape

Question 8

A cuboid has a base of 6cm, length of 4cm and height of 3cm. Find the surface area.

Answer 8

Front face: 3x6=18cm^2
Back face: 18cm^2
Left face: 3x4=12cm^2
Right face: 12cm^2
Bottom face: 6x4=24cm^2
Top face: 24cm^2

Surface area= 108cm^2

Question 9

Triangular prism. Base, 5cm. Vertical height, 6cm. Face is an isosceles Triangle. Length, 8cm. Horizontal ‘height’ 7cm. Give the surface area.

Answer 9

Front face = 6x5/2 = 15cm^2

Surface area: 182cm^2

Question 10

Give the equation for density

Answer 10

Density = mass /volume

Question 11

What is the unit for density ?

Answer 11

g/cm^3 or kg/m^3

Question 12

What do you work out for ‘capacity’?

Answer 12

Volume

Question 13

Cylinder has a horizontal base of 6cm, and a height of 8cm. Calculate the surface area

Answer 13

Working out the circumference of the circle is the base of the rectangle
Faces: two circles and a rectangle 
Top circle : pi x 3^2 = 9 pi cm^2
Rectangle : 2 pi r x 8
2 x pi x 3 x 8
48 pi cm^2

Surface area: 66 pi cm ^2 = 207.3cm^2

Question 14

Give the equation for the volume of any pyramid

Answer 14

Volume = 1/3 x area of base x height

Question 15

Find the volume of a square based pyramid, with a horizontal ‘height’ 6cm, base of 13cm

Answer 15

V = 1/3 x (12 x 12) x 6

= 1/3 x 288cm^3

Question 16

Volume of a cone = 1/3 pi r^2 h. Work out the volume of a cone, with a radius of 7cm, and vertical height of 10cm

Answer 16

V = 1/3 x pi x 7^2 x 10
= 513.126…
=513.1cm^3

Question 17

A cone has a height of 2.3cm and a volume of 43cm^3. Find its radius to 3sf, when The equation for volume of a cone = 1/3 pi r^2 h

Answer 17

43= 1/3 x pi r^2 x 2.3
/ divided by 2.3
43/2.3 = 1/3 x pi r^2 
/divided by pi
5.95101... = 1/3 r^2
/ divided by pi
17.85303... = r^2
/ square root
4.2252... = r
4.23cm=r

Question 18

The formula for volume of a sphere is 4/3 pi r ^3

A sphere has radius 5.7cm. Find its volume to 3sf

Answer 18

V = 4/3 x pi x 5.7^3
= 775.7346…
= 776cm^3

Question 19

The equation for working the curve surface area of a cone is pixrxl
Work out the surface area of a cone with a diagonal length of 10m, and a radius of 6m
a) give your answer in terms of pi
b) give answer to 3sf
c) write answer to (b) in cm^2

Answer 19

a) curved surface area = pi x 6 x 10 = 60 pi m^2
Area of circle = pi r ^2 = pi x 6^2 =36 pi m^2
Surface area = 60 pi + 36 pi = 96 pi m^2
b) 96 pi = 301.528… = 302m^2
c) 302x100^2 = 3020000cm^2
Meters^2 > cm^2 =x100^2 = x 10,000

Question 20

How do you go from meters to cm?

Answer 20

x100

Question 21

How do you go from meters^2 to cm^2?

Answer 21

x100^2 = x10,000

Question 22

How do you go from meters^3 to cm^3?

Answer 22

x100^3 = x1,000,000

Question 23

Surface area of a sphere = 4xpixr^2

Work out the surface area of a sphere with a radius of 3cm, give your answer to 1dp

Answer 23

Surface area = 4 x pi x 3^2
= 36 pi
= 113.1 cm^2

Question 24

Work out 25% of £250

Answer 24

100% = 250
10% = 25
5% = 12.50
20% = 50
25%= £62.50

Question 25

Work out 17.5% of 48kg

Answer 25

100% = 48kg
10% = 4.8kg
5% = 2.4kg
2.5% = 1.2kg
17.5% = 8.4kg

Question 26

Decrease £450 by 37.5%

Answer 26

100%=450
10%=45
5%=22.5
2.5%=11.25
30%=135
37.5%=£168.75

£450-£168.75=281.25
Ans: £281.25