Question

in the adjoining figure, the larger circle with radius 4cm is touched internaily by two smaller circles which also touch each other enternally at the centre O of the larger circle . The area of shaded portion is :
(a). 4π sq.units.
(b). 7π sq.units.
(c). 12π sq.units.
(d). 6π sq.units.​

Answer 1

Answer:

4π Sq.units.

Step-by-step explanation:

area of large semi circle:-

πr^2/2

π×4×4×1/2

π×16×1/2

π×8

therefore,8π

area of both

Area of Both Smaller semi circles:-

2×πr^2/2

πr^2

π×2×2(the radius here is 2cm as the radius of the larger circles is the diameter here so 4/2=2cm

π×4

therefore,4π

Remaining area:- Area of larger semi circle-Area of both the smaller semi circles

8π-4π

4π Sq.units.

Answer 2

Given: in the adjoining figure, the larger circle with radius 4cm is touched internaily by two smaller circles which also touch each other enternally at the centre O of the larger circle .

To find: The area of shaded portion.

Solution:

Since the larger circle has a radius of 4 cm, the two smaller circles must have a radius of 2 cm. The area of the largest circle is calculated as

$Area = \pi r^{2}$

        $= \frac{22}{7} * (4)^{2}$

        $= 16\pi cm^{2}$

The area of the two smaller circles is calculated as follows.

$A = 2 * \pi r^{2}$

   $= 2*\pi * (2)^{2}$

   $= 8 \pi cm^{2}$

Now, the area of the remaining portion is calculated as

$16\pi - 8\pi = 8\pi cm^{2}$

But only one side of the remaining portion is shaded. So, the area of the shaded portion is

$\frac{8\pi }{2} = 4\pi$

Therefore, the area of the shaded portion is 4π sq. units.

Although a figure of your question is missing, you might be referring to the one attached.