Question

The diameter of a circular stadium is 42 m. Calculate
the cost of maintaining the ground of the stadium at the
rate Sr.230/m2 and also find the cost of fencing the
playground at the rate of Sr. 90/m2


The diameter of a circular stadium is 42 m. Calculate
the cost of maintaining the ground of the stadium at the
rate Sr.230/m2 and also find the cost of fencing the
playground at the rate of Sr. 90/m2

Answer 1

Correct Question :

The diameter of a circular stadium is 42 m. Calculate  the cost of maintaining the ground of the stadium at the  rate of Rs. 230/m² and also find the cost of fencing the playground at the rate of Rs. 90/m².

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⇒ Part 1

Before, finding the answer. Let's find out on how we can find the answer.

• We have to first find the Radius of the Circle by dividing it by 2.

• Now, we have to find the Area of the Circle by using the formula of :

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

• After finding the Area, we should multiply both the Rate and Area.

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⇒ Part 2 :

• So here, we have to find the Circumference of Circle, we must use the formula of :

$\boxed{\sf Circumference \: of \: Circle = 2 \pi r }$

• After finding the Circumference, we have to multiply both Rate and Circumference.

________________________

Given :

• Diameter = 42 m
• Cost for Maintaining = Rs. 230 m²

Solution :

Diameter =  radius × 2

$\sf = \dfrac{diameter}{2}$

$\sf = \dfrac{42}{2}$

$\sf = 21$

Hence, Radius is 21 m.

→ Area of Circle = πr² [Where, π is $\sf = \frac{22}{7}$ ]

                       = $\sf \dfrac{22}{7} \times 21^{2}$

                       $\sf = \dfrac{22}{7} \times 441$

                       $\sf = \dfrac{9261}{7}$

                      $\sf = 1323 m^{2}$

Hence, Area of Circle is 1323 m².

→ Cost for Maintaining = Area × Rate

                                  = 1323 × 230

                                  = Rs. 304290

∴ Cost for Maintaining is Rs. 304290.

_____________________

→ Circumference of Circle = 2πr

                                        = 2 × radius × $\frac{22}{7}$

                                        = 2 × 21 × $\frac{22}{7}$

                                        = 42 × $\frac{22}{7}$

                                        = $\dfrac{968}{7}$

                                        = 138.2 m

Hence, Circumference of Circle is 138.2 m.

→ Cost for Fencing = Rate × Circumference

                               = 90 × 138.2

                               = Rs. 12438

∴ Cost for Fencing is Rs. 12438.