Question

If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the large circle (in cm) is
(a)34
(b)26
(c)17
(d)14

Answer 1

Answer:

The diameter of a bigger circle is 26 cm

Among the given options option (b) 26 cm is the correct answer.

Step-by-step explanation:

Given :

Let ‘d’ be the diameter of a bigger circle.

Area of bigger circle , A =  Area of circle having diameter 10 cm +  Area of circle having diameter 24 cm

π(d/2)² = π(10/2)² + π(24/2)²

[Area of circle = πr² =  π(d/2)²]

π(d/2)² = π(5)² + π(12)²

π(d/2)² = π [(5)² +(12)²]

(d/2)² = 25 + 144

(d/2)² = 169

(d/2) = √169

(d/2) = 13

d = 13 × 2

d = 26 cm

Diameter of a bigger circle = 26 cm

Hence, the diameter of a bigger circle is 26 cm

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\huge\underline\mathcal\green{Answer}$

The correct answer is option (b) 26 .

The diameter of the larger circle is 26 cm .

$\huge\underline\mathcal\green{Solution}$

Let the diameter of the bigger circle be d cm .

And it is given that the diameter of the other two circles are 10cm and 24cm .

Now , According to the question ,

Area of circle with diameter d cm = area of circle with diameter 10 cm + area of circle with diameter 24 cm .

$= \pi (\frac{d}{2})^{2} = \pi( \frac{10}{2} )^{2} + \pi (\frac{24}{2} )^{2}$

$= \pi (\frac{d}{2} )^{2} = \pi( {5})^{2} + \pi( {12})^{2}$

$= \pi (\frac{d}{2} )^{2} = \pi(25 + 144)$

$= ( \frac{d}{2} )^{2} = 169$

$= \frac{ {d}^{2} }{4} = 169$

$= {d}^{2} = 169 \times 4$

$= {d}^{2} = 676$

$= d = 26 \: cm$

Hence , the diameter of the larger circle is 26 cm .