CAIE IGCSE Mathematics Extended E5.4 Surfac…olume

Covered syllabus points

E5.4.1 Carry out calculations and solve problems involving the surface area

[Maximum number: 6]

(a)

NOT TO SCALE

The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17 cm . Both ends of the cylinder touch the curved surface of the sphere.

[ 6 ]

(i)

Show that the height of the cylinder is 30 cm .

[ 2 ]

$2\sqrt{17^2-8^2}$ or $\sqrt{34^2-16^2}$ oe
M1 for $17^2=8^2+d^2$ or $34^2=16^2+k^2$

(ii)

Calculate the volume of the cylinder as a percentage of the volume of the sphere.
[The volume, V, of a sphere with radius r is V=4/3 r^3.]

[ 4 ]

29.3 or 29.30 to 29.31
M3 for $\frac{\pi\times8^2\times30}{\frac43\pi\times17^3}\times100$ oe
OR M1 for $\pi\times8^2\times30$ oe
M1 for $\frac43\pi\times17^3$ oe

[Maximum number: 10]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

A cone has base diameter 8 cm and perpendicular height 15 cm .

[ 7 ]

(i)

Calculate the volume of the cone.
[The volume, V, of a cone with radius r and height h is $V=\frac{1}{3} \pi r^{2} h$ .]

[ 2 ]

251 or 251.3 to 251.4

2

M1 for $\frac{1}{3} \times \pi \times 4^{2} \times 15 \mathrm{oe}$

(ii)

A label completely covers the curved surface area of the cone.

Calculate the area of the label as a percentage of the total surface area of the cone. [The curved surface area, A, of a cone with radius r and slant height l is $A=\pi r l$ .]

[ 5 ]

79.5 or 79.51
M3 for $\pi\times4\times\sqrt{4^2+15^2}$ oe, or M2 for $15^2+4^2$ oe, or M1 for $l^2=4^2+15^2$ or $\pi\times4\times\text{their }l$
M1 for $\frac{\text{their curved surface area}}{\text{their curved surface area}+\pi\times4^2}\times100$ oe

(b)

NOT TO SCALE

An empty cylindrical container has radius 0.45 m . 300 litres of water is poured into the container at a rate of 375 ml per second.

[ 3 ]

(i)

Calculate the height of the water in the container. m

[ 3 ]

0.472 or 0.4715 to 0.4716
M2 for $\pi\times0.45^2\times h=0.3$ or $\pi\times45^2\times h=300000$ oe, or M1 for $\pi\times\text{figs }45^2\times h=\text{figs }3$ oe

[Maximum number: 5]

Solid A

Solid B

In this question all measurements are in centimetres.

NOT TO SCALE

Solid A is made from a cylinder and a hemisphere, both of radius 2R.
The cylinder has height 5R.
Solid B is a cone of radius R and sloping edge x.
The total surface area of solid A is equal to the total surface area of solid B.
Find R in terms of x.
R=

$R=\frac{x}{31}$

M1 for $\pi(2R)^2$ oe
M1 for $2\pi(2R)(5R)$ oe
M1 for $\frac{4\pi(2R)^2}{2}$ oe
M1 for $\pi Rx+\pi R^2$ oe

All question bank results loaded

CAIE IGCSE Mathematics Extended E5.4 Surface Area and Volume Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question 3