MCQ
Choose the correct answer from the given four options : The radius of a circle whose circumference is equal to the sum of the circumferences of two circles of diameters $36\ cm$ and $20\ cm$ is :
- A$56\ cm$
- B$42\ cm$
- ✓$28\ cm$
- D$16\ cm$
✓
Answer
Correct option: C.
$28\ cm$
$\because$ Circumference of first circle $=2\pi\text{r}=\pi\text{d}_1=36\pi\text{ cm}\ [$given, $\mathrm{d}_1 = 36\ cm]$
and circumference of second circle $=\pi\text{d}_2=20\pi\text{ cm}\ [$given, $\mathrm{d}_2 = 20\ cm]$
According to the given condition,
Circumference of circle $=$ Circumference of first circle $+$ Circumference of second circle
$\Rightarrow \pi\text{D}=36\pi+20\pi \ [$where $,D$ is diameter of a circle$]$
$\Rightarrow \text{D}=56\text{ cm}$
So, diameter of a circle is $56\ cm.$
$\therefore$ Required radius of circle $\frac{56}{2}=28\text{ cm}$
and circumference of second circle $=\pi\text{d}_2=20\pi\text{ cm}\ [$given, $\mathrm{d}_2 = 20\ cm]$
According to the given condition,
Circumference of circle $=$ Circumference of first circle $+$ Circumference of second circle
$\Rightarrow \pi\text{D}=36\pi+20\pi \ [$where $,D$ is diameter of a circle$]$
$\Rightarrow \text{D}=56\text{ cm}$
So, diameter of a circle is $56\ cm.$
$\therefore$ Required radius of circle $\frac{56}{2}=28\text{ cm}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $\tan ^2 A=1+2 \tan ^2 B$, then $\frac{\cos ^2 A}{\cos ^2 B}=$
→If value of each observation in a data is increased by 2, then the median of the new data
In triangles ABC and DEF, $\angle\text{A}=\angle\text{E}=40^\circ,$ AB : ED = AC : EF and $\angle\text{F}=65^\circ,$ then $\angle\text{B}=$
→The value of $\cos1^\circ\cos2^\circ\cos3^\circ.....\cos180^\circ$ is :
→If $A$ is an acute angle in a right triangle $A B C$, right angled at $B$, then the value of $\sin A+\cos A$ is
→Which term of the A.P. $-29,-26,-23$, ...., 61 is 16 ?
→Choose the correct answer from the given four options : While computing mean of grouped data, we assume that the frequencies are :
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}$ is equal to :
→A circle has its centre at the origin and a point $P(5, 0)$ lies on it. Then the point $Q(8, 6)$ lies $..........$ the circle.
→The volume of a cube is $2744 \ cm ^3$. Its surface area is
→