Question

The area of a circle is 40 times the area of a triangle whose base is 88cm and height is 35 cm. find the radius of circle and also its circumference
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Answer 1

Concept of the question :-

Question is given from Areas and Perimeter of 2 Dimensional shapes in which their are two shapes Triangle and circle. Circle has Area of 40 times larger than Area of triangle whose base length is 88 cm and height length is 35 cm. We need to find Radius and circumference of circle.

Assumption :-

• Let x be the area of triangle then circle has Area = x × 40 because its area is 40 times greater.

Given :-

• Area of circle = x × 40 cm²
• Area of the triangle = x
• Base of triangle = 88 cm
• Height of triangle = 35 cm

To find :-

• Radius of Circle
• Circumference of circle.

Formula to be used :-

❶ Area of triangle

${\boxed{\sf{ Area = \frac{1}{2} \times Base \times Height }}}$

❷ Area of circle

${\boxed{\sf{Area = \pi {r}^{2} }}}$

❸ To find circumference of Circle

${\boxed{\sf{Circumference = 2\pi r }}}$

Solution :-

✯ Area of the triangle is

${\sf{\implies{ \cfrac{1}{2} \times Base \times Height }}}$

${\sf{\implies{ \cfrac{1}{2} \times 88 \times 35 }}}$

${\sf{\implies{ 1 \times 44 \times 35 }}}$

${\sf{\implies{ \underline{ 1540 \: {cm}^{2} }}}}$

✯ Area of the circle is

${\sf{\implies {Area = x \times 40}}}$

Here value of x is the 1540 because as above given

${\sf{\implies {Area = 1540 \times 40}}}$

${\sf{\implies{ \underline {Area = 61600 \: {cm}^{2} }}}}$

✯ Radius of the circle is :-

${\large{\sf{ \ratio\longmapsto{Area \: of \: circle = \pi {r}^{2} }}}}$

${\large{\sf{ \ratio\longmapsto{61600= \cfrac{22}{7} \times {r}^{2} }}}}$

${\large{\sf{ \ratio\longmapsto{ \cfrac{61600 \times 7}{22} = \times {r}^{2} }}}}$

${\large{\sf{ \ratio\longmapsto{ \cfrac{431200}{22} = {r}^{2} }}}}$

${\large{\sf{ \ratio\longmapsto{ 19600 = {r}^{2} }}}}$

${\large{\sf{ \ratio\longmapsto{ {r}^{2} = \sqrt{19600} }}}}$

${ \underline{ \overline{ \boxed{\large{ \red{\sf{ \ratio\longmapsto{ r = 140 \: cm \: }}}}}}}}$

✯ Circumference of circle

${\large{\sf{ \ratio\longmapsto{Circumference = 2\pi r}}}}$

${\large{\sf{ \ratio\longmapsto{Circumference = 2 \times \cfrac{22}{7} \times 140}}}}$

${\large{\sf{ \ratio\longmapsto{Circumference = 2 \times 22 \times 20}}}}$

${\large{\sf{ \ratio\longmapsto{Circumference = 44 \times 20}}}}$

${\large{ \underline{ \overline{ \boxed{ \red{\sf{ \ratio\longmapsto{Circumference = 880 \: cm}}}}}}}}$

Final answer :-

So area the circle is 61600 cm , Radius is 140 cm and circumference is 88 cm.