Question

the area of a circle is 40 times the area of a triangle whose base is 88 cm and height is 35 cm find the radius of the circle and its circumference​

Answer 1

Given :

The area of a circle is 40 times the area of a triangle whose base is 88 cm and height is 35 cm.

To FinD :

The radius of the circle and its circumference.

Solution :

Analysis :

Here the formula of Area of triangle, area of circle and circumference of circle is used. First we have find the area of the triangle. Then from that area of triangle we can evaluate the area of the circle. After that by using the formula of the area of circle we can find the radius and by using the value of radius and the formula of circumference we can take out our final answer i.e., the circumference of the circle.

Required Formula :

• Area of triangle = 1/2 × Base × Height

• Area of circle = πr²

• Circumference of circle = 2πr

where,

• r = Radius
• π = 22/7 or 3.14

Explanation :

The area of Triangle :

We know that if we are provided with the base of the triangle and the height of the triangle and is asked to find a area of triangle then our required formula is,

Area of triangle = 1/2 × Base × Height

where,

• Base = 88 cm
• Height = 35 cm

Using the required formula and substituting the required values,

⇒ Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 1/2 × Base × Height

⇒ Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 1/2 × 88 × 35

⇒ Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 1 × 44 × 35

⇒ Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 44 × 35

⇒ Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 1540

∴ Area of triangle = 1540 cm².

Area of circle :

It is said that the area of circle is 40 times the area of triangle.

So,

☯ According to the question,

⇒ Area₍꜀ᵢᵣ꜀ₗₑ₎ = 40 × Area₍ₜᵣᵢₐₙ₉ₗₑ₎

where,

• Area₍ₜᵣᵢₐₙ₉ₗₑ₎ = 1540 cm²

Putting the values,

⇒ Area₍꜀ᵢᵣ꜀ₗₑ₎ = 40 × 1540

⇒ Area₍꜀ᵢᵣ꜀ₗₑ₎ = 61600

∴ Area of circle = 61600 cm².

Let us assume that radius of the circle is "r" cm.

• Area₍꜀ᵢᵣ꜀ₗₑ₎ = 61600 cm²

We know that if we are provided with the area of the circle and is asked to find out the radius of the circle then our required formula is,

Area of circle = πr²

where,

• π = 22/7 or 3.14
• Area₍꜀ᵢᵣ꜀ₗₑ₎ = 61600 cm²
• r = r cm

Using the required formula and substituting the required values,

⇒ Area₍꜀ᵢᵣ꜀ₗₑ₎ = πr²

⇒ 61600 = 22/7 × r²

⇒ 61600 × 7/22 = r²

⇒ 431200/22 = r²

⇒ 19600 = r²

Square rooting both the sides,

⇒ √19600 = r

⇒ √[140 × 140] = r

⇒ 140 = r

∴ Radius of circle = 140 cm².

Verification :

⇒ Area₍꜀ᵢᵣ꜀ₗₑ₎ = πr²

⇒ 61600 = 22/7 × (140)²

⇒ 61600 = 22/7 × 140 × 140

⇒ 61600 = 22 × 20 × 140

⇒ 61600 = 440 × 140

⇒ 61600 = 61600

∴ LHS = RHS.

• Hence verified.

Circumference :

We know that if we are provided with the radius of the circle and is asked to find out the circumference of the circle then our required formula is,

Circumference of circle = 2πr

where,

• π = 22/7 or 3.14
• r = 140 cm

Using the required formula and substituting the required values,

⇒ Circumference of circle = 2πr

⇒ Circumference of circle = 2 × 22/7 × 140

⇒ Circumference of circle = 2 × 22 × 20

⇒ Circumference of circle = 880 cm

∴ Circumference of the circle = 880 cm.

Radius of circle is 140 cm.

Circumference of the circle is 880 cm.

Answer 2

GivEn:

• Area of Circle is 40times the area of triangle.
• Base of triangle = 88cm
• height of triangle = 35cm

To finD:

• Radius of Circle
• Circumference of Circle

Solution:

First of all we have given that area of Circle is 40 times the area of triangle. So, firstly we will calculate the area of triangle and then area of Circle.

Finding area of triangle :

In this triangle, we have given base and height of triangle are 88cm and 35cm respectively. To find area, the required formula is as :-

Formula using :

Area of triangle = 1/2 × base × height

Where,

• base = 88cm •••••(given)
• height = 35cm •••••( given)

Let put the values in formula:-

Substituting values in formula:

Area of triangle = 1/2 × base × height

⇒Area of triangle = 1/2 × 88 × 35

⇒Area of triangle = 3080/2

⇒Area of triangle = 1540cm²

● So, the area of triangle is 1540cm²

Finding area of Circle :

It is given that area of Circle is 40 times the area of triangle.

Hence,

Area of triangle = 1540cm² •••( find in above explanation)

So,

Area of Circle = 40× area of triangle

⇒ Area of Circle = 40× 1540

⇒Area of Circle = 61600cm²

● So, the area of Circle is 61600cm²

Now, we found that area of triangle and area of Circle.

Let us finding the radius of Circle and circumference of Circle.

Finding radius of Circle :-

we have given area of Circle is 61600cm².

We know that:

Area of Circle = πr²

Where,

• Area of Circle = 61600cm² •••( given}
• π = 22/7
• r = radius of Circle •••( find)

Let put the values in this formula :

Area of Circle = πr²

⇒61600 = 22/7×r²

⇒r² = 61600×7/22

⇒r² = 431200/22

⇒r² = 19600

⇒r = √19600

⇒r = 140

⇒r = 140cm

● so, The radius of Circle = 140cm

Finding Circumference of Circle :

To find the circumference of Circle, the required formula is :

Formula using:-

Circumference of Circle = 2πr

Where,

• π = 22/7
• r = radius of Circle => 140cm ••• find in above explanation)

Let put the values in this formula to find circumference.

Substituting values in formula :-

Circumference of Circle = 2πr

⇒Circumference of Circle = 2×22/7×140

⇒Circumference of Circle = 6160/7

⇒Circumference of Circle = 880

⇒Circumference of Circle = 880cm

● So, circumference of Circle = 880cm

OUR REQUIRED ANSWER :-

• Radius of Circle = 140cm
• Circumference of Circle = 880cm