Question

the circumference of a circle exceeds the diameter by 90cm. find the radius, diameter and circumference​

Answer 1

Answer:

• Radius = 21 cm
• Diameter = 42 cm
• Circumference = 132 cm

Step-by-step explanation:

Given :

The circumference of a circle exceeds the diameter by 90cm.

To find :

the radius, diameter and circumference.

Solution :

Let the diameter of the circle be 'd' cm and radius be 'r' cm.

We know,

Circumference of the circle = 2πr = πd

    $\sf \pi d = d + 90 \\ \sf \pi d - d = 90 \\ \sf d(\pi - 1) = 90 \\ \sf d\bigg(\dfrac{22}{7}-1 \bigg) = 90 \\ \sf d\bigg(\dfrac{15}{7}\bigg)=90 \\ \sf d=90 \times \dfrac{7}{15} \\ \sf d=6 \times 7 \\ \sf d=42 \: cm$

∴ The diameter of the circle is 42 cm.

• The radius is half the diameter.

r = d/2 = 42/2 = 21 cm

• The circumference of the circle = πd

C = 22/7 × 42

C = 22 × 6

C = 132 cm