Question

Q65 The radius of a circle is 8 cm. Determine
the radius of another circle whose area is
16 times of the first circle.
Ops: A. 16.2 cm
B. 32.2 cm
C.
16 cm
D. 32 cm​

Answer 1

Answer:

• Option (d) is correct, Radius of another circle is 32 cm.

Step-by-step explanation:

Given that,

Radius of first circle is 8 cm.

We know,

Area of circle = πr²

$\longrightarrow$ Area = 22/7 × (8)²

$\longrightarrow$ Area = 22/7 × 64

$\longrightarrow$ Area = 1408/7

Thus,

Area of first circle is 1408/7 cm².

Now,

It is also given that Area of another circle is 16 times of first circle

$\longrightarrow$ 1408/7 × 16

$\longrightarrow$ 22528/7

Area of another circle is 22528/7 cm².

Now,

$\longrightarrow \sf \pi r^{2} = \dfrac{22528}{7}$

$\longrightarrow \sf \dfrac{22}{7} \times r^{2} = \dfrac{22528}{7}$

$\longrightarrow \sf r^{2} = \dfrac{22528 \times \cancel{7} }{\cancel{7} \times 22}$

$\longrightarrow \sf r^{2} = \dfrac{22528}{22}$

$\longrightarrow \sf r^{2} = 1024$

$\longrightarrow \sf r = \sqrt{1024}$

$\longrightarrow \pmb{\sf{r = 32}}$

∴ Radius of another circle is 32 cm.

Answer 2

Answer:

Given :-

Radius of circle is 8 cm

To Find :-

Radius of other circle

Solution :-

Area of second circle = 16 × Area of first circle

=> Area of circle = πr²

Area of first circle = π × (8)²

Area of first circle = π × 64

Area of first circle = 64π cm²

Now

Since second circle is 16 times the first one

Area of second circle = 16 × 64π

Area of second circle = 1024π cm²

According to the question

πr² = 1024π

r² = 1024

r = √(1024)

r = 32

Hence,

Radius is 32 cm