Question

The circumference of a circle is equal to the sum of the circumference of two circles having diameters 36 cm and 20 cm. The radius of the new circle is
(a) 16 cm
(b) 28 cm
(c) 42 cm
(d) 56 cm

Answer 1

(b) 28 cm
Let r cm be the radius of the new circle.
We know:
Circumference of the new circle = Circumference of the circle with diameter 36 cm + Circumference of the circle with diameter 20 cm
Thus, we have:
$2\pi r=2\pi r_1+2\pi r_2$
$$\begin{gathered} \Rightarrow 2\pi r=\left(2\pi \times 18\right)+\left(2\pi \times 10\right) \\ \Rightarrow 2\pi r=2\pi \times \left(18+10\right) \\ \Rightarrow 2\pi r=\left(2\pi \times 28\right) \\ \Rightarrow 2\pi r=\left(2\times \frac{22}{7}\times 28\right) \end{gathered}$$
$$\begin{gathered} \Rightarrow 2\pi r=176 \\ \Rightarrow 2\times \frac{22}{7}\times r=176 \\ \Rightarrow r=\left(176\times \frac{7}{44}\right) \\ \Rightarrow r=28\mathrm{cm} \end{gathered}$$