Question

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?​

Answer 1

Given:

• We're given with Two circles having diameters of 10 cm and 24 cm.

To find:

• Diameter of the circle.

Solution:

As we know that,

★ Area of Circle = πr² ★

Now, A/Q

• Area of required circle = Area of circle of Diameter of 10 cm + Area of circle with diameter of 24 cm.

Therefore,

➟ πr² = π(5)² + π(12)²

➟ πr² = 25π + 144π

➟ πr² = 169π

• (Cancelled both π)

➟ r² = 169

➟ r = √169

➟ r = 13 cm

• (Diameter = 2 × radius)

➟ Diameter = 2(13)

➟ Diameter = 26 cm

•°• Diameter of required circle is 26 cm.

Answer 2

Answer:

The diameter of the circle is 26cm

Step-by-step explanation:

Question:

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?

Given:

$\star\;\underline{\boxed{\sf{\pink{Area\ of\ Circle\ =\ \bf Area\ of\ Circle\ of\ diameter\ 10cm + \ Area\ of\ circle\ of \ diameter\ 24\ cm}}}}$

To find:

$\looparrowright$ $\sf{Diameter\:of\:the\:circle}$

Solution:

Area of circle = $\mathtt{πr^2}$

$\bf{\green{πr^2 = π(5)^2 + π(12)^2}}$

$\bf{\green{πr^2 = 25π+ 144π}}$

$\bf{\green{πr^2 = 169π}}$

$\bf{\green{ \cancelπr^2 = 169 \cancelπ}}$

$\bf{\green{ r^2 = 169 }} \\ \\ \bf{ \green{r = 13cm}}$

D = 2r

D = 26cm

Hence, the diameter of the circle is 26cm