The diameter of a circle whose area is equal | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let $r_{1}=24\, cm$ and $r _{2}=7 \,cm$

$	herefore$ Area of first circle $=\pi r_{1}^{2}=\pi(24)^{2}=576 \pi \, cm ^{2}$

and area of second cir

Vedclass · Accepted Answer

$50$

Vedclass · Answer

Let $r_{1}=24\, cm$ and $r _{2}=7 \,cm$

$	herefore$ Area of first circle $=\pi r_{1}^{2}=\pi(24)^{2}=576 \pi \, cm ^{2}$

and area of second circle $=\pi r_{2}^{2}=\pi(7)^{2}=49 \pi\, cm ^{2}$

According to the given condition, Area of circle $=$ Area of first circle $+$ Area of second circle

$	herefore$ $\pi R^{2}=576 \pi+49 \pi$ [where, $R$ be radius of circle $]$

$\Rightarrow$ $R^{2}=625 \Rightarrow R=25 \,cm$

$	herefore$ Diameter of a circle $=2 R=2 	imes 25=50 \,cm$

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24 \,cm$ and $7 \,cm$ is (in $cm$)

Similar Questions

The circumference of a circle is $176 \,cm .$ Find its radius. (in $cm$)

The radius of a circular ground is $56\,m.$ A $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40 / m ^{2}$ (in ₹)

The ratio of radii of two circles is $2: 3$ and the ratio of the angles at centre of two minor sectors of those circles is $5: 2 .$ Then, the ratio of the areas of those sectors is...........

In a circle with radius $6.3\, cm ,$ a minor arc subtends an angle of measure $40$ at the centre. The area of the minor sector corresponding to that arc is $\ldots \ldots cm^{2}$.

With the vertices $A , B$ and $C$ of a triangle $ABC$ as centres, arcs are drawn with radii $5 \,cm$ each as shown in $Fig.$ If $AB =14 \,cm , BC =48 \,cm$ and $CA =50\, cm ,$ then find the area of the shaded region. (Use $\pi=3.14)$ (in $cm^2$)