Question

The area of a circle is equal to the sum of the areas of two circles of diameters
10 cm and 24 cm.
Find the:
(1)
diameter
(u)
circumference of the larger circle.
(Take n = 3.1)​


please answer fast

Answer 1

Answer:

Diameter of the larger circle is 26 cm and Circumference of the larger circle is 80.6 cm

Step-by-step explanation:

Area of circle is $A=\pi r^2$

Area of first circle whose diameter is 10 cm , radius is 5 cm

$A_{1}=\pi r_{1}^2\\A_{1}=\pi \times {5}^2\\A_{1}=25\pi cm^2$

Area of second circle whose diameter is 24 cm , radius is 12 cm

$A_{2}=\pi r_{2}^2\\A_{1}=\pi \times {12}^2\\A_{1}=144\pi cm^2$

The area of a circle is equal to the sum of the areas of two circles. ie

$A=A_{1}+A_{2}\\\pi r^2=25\pi +144\pi \\\pi r^2=169\pi \\r^2=169\\r=\sqrt{169} \\r=13 cm$

Diameter of the larger circle is $d=2r =2\times13 =26 cm$

Circumference of the larger circle is

$=2\pi r=2\times 3.1 \times 13=80.6 cm$