Question

9. In Akshita’s house there is a flower pot. The sum of radii of circular top and bottomof a flowerpot is 140 on and the difference of their circumference is 88cm. find thediameter of the circular top and bottom.
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Answer 1

Given :-

• In Akshita’s house there is a flower pot. The sum of radii of circular top and bottom of a flowerpot is 140cm on and the difference of their circumference is 88cm.

To find :-

• Diameter of the circular top and bottom.

Solution :-

It is given in Akshita’s house there is a flower pot. It means one circle at top and other circle at bottom of a flower pot.

Now, let the bigger radius be R and smaller radius be r of flower pot

According to the question

• Sum of radii of flower pot = 140cm

→ R + r = 140 ----(i)

• Difference of their circumference is 88cm.

As we know that

Circumference of circle = 2πr

Here, there are two circle so circumference of circles

→ 2πR + 2πr

But in question it is given that the difference between their circumference is 88

So,

→ 2πR - 2πr = 88

Take 2π as a common

→ 2π(R - r) = 88

→ R - r = 88/2π

→ R - r = 44/π

→ R - r = 44/22/7

→ R - r = 44 × 7/22

→ R - r = 2 × 7

→ R - r = 14 ----(ii)

Add both the equations

→ (R + r) + (R - r) = 140 + 14

→ R + r + R - r = 154

→ 2R = 154

→ R = 154/2

→ R = 77 cm

Now , put the value of R in eqⁿ (ii)

→ R - r = 14

→ 77 - r = 14

→ r = 77 - 14

→ r = 63cm

Hence,

• Bigger radius = 77cm
• Smaller radius = 63cm

• Radius = 2 × diameter
• Diameters of pot = 154cm and 126cm

Answer 2

Question:-

In Akshita's house there is a flower pot. The sum of radii of circular top and bottom of a flowerpot is 140cm and the difference of their circumference is 88cm. Find the diameter of the circular top and bottom.

Formula Used:-

• Circumference of a circle = 2 * π * Radius
• Diameter = 2 * radius

Answer:-

Let the bigger radius be R and the smaller radius be r

Given: Sum of the radii is 140cm

So, R + r = 140 --------- (i)

Given: Difference of their circumference is 88cm So, 2πR - 2πr = 88

=> 2π(R - r) = 88

=> R - r = (88) / 2π

=> R - r = [88] / [2* (22/7)]

=> R - r = (88 * 7) / (2 * 22)

=> R - r = 14 -------- (ii)

(i) + (ii) :-

R + r + R - r = 140 + 14

=> 2R = 154

=> R= 77 cm

From (ii) :-

r = R - 14

=> r = 77 - 14

=> r = 63 cm

So diameters:-

• Larger diameter = 2R = (2 * 77) cm = 154 cm
• Smaller diameter = 2r = (2 * 63) cm = 126 cm