Question
A circle has an area of $36\pi \rm{cm}^2$ .
(a) Find the circumference of the circle.
Give your answer in terms of $\pi $.
(b) The circle forms the base of a cylinder with height h cm.
The volume of the cylinder is $540\pi \rm{cm}^3$ .
Work out the value of h.
▶️Answer/Explanation
(a) $12\π$
(b) $15$
$
A = \pi r^2
$
$
36\pi = \pi r^2
$
$
36 = r^2
$
$
r = 6 \, \mathrm{cm}
$
circumference formula
$
C = 2\pi r
$
$
C = 2\pi(6)
$
$
C = 12\pi \, \mathrm{cm}
$
(b)
$
V = \pi r^2 h
$
$
540\pi = \pi(6^2)h
$
$
540\pi = \pi(36)h
$
$
540 = 36h
$
$
h = 15 \, \mathrm{cm}
$
Question
The diagram shows a small circle with radius 7cm and a large circle with radius Rcm.
The area of 16 small circles is the same as the area of one large circle.
Calculate the value of R.
▶️Answer/Explanation
28
area of a circle is
$
A = \pi r^2
$
small circle, the radius is 7 cm,
$
\text{Area of small circle} = \pi (7^2) = 49\pi \text{ cm}^2
$
Since the area of 16 small circles equals the area of the large circle,
$
\text{Total area of 16 small circles} = 16 \times 49\pi = 784\pi \text{ cm}^2
$
$
\text{Area of large circle} = \pi R^2
$
$
\pi R^2 = 784\pi
$
$
R = \sqrt{784}
$
$
R = 28
$
Question
The diagram shows a circular disc with radius 6 cm.
In the centre of the disc there is a circular hole with radius 0.5 cm.
Calculate the area of the shaded section.
Answer/Explanation
Ans: 112 or 112.3 to 112.33
Question
The diagram shows a circle, centre O.
P, Q and R are points on the circumference.
PQ = 17 cm and QR = 9cm.
(a) Explain why angle PQR is 90°.
Answer/Explanation
Ans: Angle [in a] semi-circle
(b) Calculate the length PR.
Answer/Explanation
Ans: 19.2 or 19.23 to 19.24
Question
In the diagram, AP is a tangent to the circle at P.
O is the centre of the circle, angle PAO = 37° and AP = 11cm.
(a) Write down the size of angle OPA.
Answer/Explanation
Ans: 90
(b) Work out the radius of the circle.
Answer/Explanation
Ans: 8.29 or 8.289 to 8.29
Question
The diagram shows a circle, centre O.
A, B and C are points on the circumference.
Write down the mathematical name of the straight line
(a) OC,
Answer/Explanation
Ans: radius
(b) AB.
Answer/Explanation
Ans: chord