Question

if the area of a circle is equal to the sum of the two circles of diameter 10 cm and 24 cm and the diameter of the largest circle is

Answer 1

area of circle of diameter 10 = $\pi$*(5)² = 25$\pi$

area of circle of diameter 24 = $\pi$(12)² = 144$\pi$

area of larger circle = 25$\pi$ + 144$\pi$ = 169$\pi$

$\pi r^{2}$ = 169$\pi$

$r^{2}$ = 169

r=13

thus d=13*2 = 26cm

Answer 2

Find the area of the circle with diameter 10 cm

Radius = Diameter ÷ 2

Radius = 10 ÷ 2 = 5 cm

Area = πr²

Area = π(5)² = 25π cm²

Find the area of the circle with diameter 24 cm

Radius = Diameter ÷ 2

Radius = 24 ÷ 2 = 12 cm

Area = πr²

Area = π(12)² = 144π cm²

Find the area of the larger circle:

Area = 144π + 25π = 169π cm²

Find the radius:

Area = πr²

πr² = 169π

r² = 169

r = √169

r = 13 cm

Find the diameter:

Diameter = Radius x 2

Diameter = 13 x 2 = 26 cm

Answer: The diameter is 26 cm