A sector of a circle of radius 7cm subtending an angle of 270° at the centre of the circle is used to form a cone. (a) Find the base radius of the cone. (b)...
Question 1 Report
A sector of a circle of radius 7cm subtending an angle of 270° at the centre of the circle is used to form a cone.
(a) Find the base radius of the cone.
(b) Calculate the area of the base of the cone to the nearest square centimetre.
[Take \(\pi = \frac{22}{7}\)]
Answer Details
When a sector is rolled into a cone, the arc length of the sector becomes the circumference of the cone's base, and the sector radius becomes the slant height.
(a) Arc length \(=\dfrac{270}{360}\times2\pi\times7=\dfrac{3}{4}\times2\times\dfrac{22}{7}\times7=\dfrac{3}{4}\times44=33\text{ cm}.\)
Base circumference \(=2\pi r=33\):
\[2\times\frac{22}{7}\times r=33\Rightarrow\frac{44}{7}r=33\Rightarrow r=\frac{33\times7}{44}=5.25\text{ cm}.\]
Base radius \(=5.25\) cm.
(b) Base area \(=\pi r^{2}=\dfrac{22}{7}\times(5.25)^{2}=\dfrac{22}{7}\times27.5625=86.625\text{ cm}^{2}\).
\(\approx 87\text{ cm}^{2}\) (nearest square centimetre).
Download The App On Google Playstore
Everything you need to excel in your exams
