Class X Session 2023-24 Question 15

 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 15

It is proposed to build a new circular park equal in area to the sum of areas of two circular

parks of diameters 16 m and 12 m in a locality. The radius of the new park is

(a) 10m 

(b) 15m 

(c) 20m 

(d) 24m

Explanation : 

we first need to calculate the areas of the two circular parks with diameters of 16 m and 12 m, respectively.Then, we can find the sum of these areas.

Let's calculate

\[ Area \; of\; the\; circular\; park\; with\; diameter \;16 m\; =\; \pi\times \frac{16^2}{2^2} = \pi\times 8^2 m^2 \]

\[ Area \; of\; the\; circular\; park\; with\; diameter \;12 m\; =\; \pi\times \frac{12^2}{2^2} = \pi\times 6^2 m^2 \]

\[ Now,\; we \;find\; the \; Total \;Area\; =\; \pi\times 64 + \pi\times 36 \; = 100 \pi m^2 \]

To find the radius of the new park with an area equal to 100𝜋m^2 , we use the formula for the area of a circle

 => Total area = 𝜋 r^2 

=> 100𝜋 = 𝜋r^2

=> Or r^2 = 100

=> Or r = 10 m

The diagram below will appear if we take into consideration circles with diameters of 16 m for r1 and 12 m for r2.

Guess the Option and comment below  👇