EXERCISE 12.1

QUESTION 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Answer

Here r1 = 19 cm => Circumference of circle ist = 2 x π x 19 = 38π

         r2 = 9 cm  => Circumference of circle 2nd = 2 x π x 9 = 18π

Let radius of third circle = R => Circumference of circle 3rd = 2 x π x R = 2πR

By  the question

Circumference of Third circle = Circumference of circle ist + Circumference of circle 2nd

=> 2πR  = 38π + 18π

=> 2πR  = 56 π

=> R = 28

hence radius of third circle = 28cm.

QUESTION 2: The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer

Let the radius of the third circle be R.
Area of the circle with radius R = πR²
Area of the circle with radius 8 cm = π × 8² = 64π cm²
Area of the circle with radius 6 cm = π × 6² = 36π cm²
Sum of the area of two circles = 64π cm² + 36π cm² = 100π cm²
Area of the third circle = πR² = 100π cm²
⇒ πR² = 100π cm²
⇒ R² = 100 cm²
⇒ R = 10 cm

Thus, the radius of the new circle is 10 cm.

QUESTION3: Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

                                                                                                                 

Answer

QUESTION 4: The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour? 

Answer

Number of revolutions = (𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒)/(𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑 𝑖𝑛 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛) 

Diameter of circle = 80 cm radius = r = 80/2 = 40 cm 

Distance covered in one revolution = Circumference of wheel = 2 𝜋r = 2 ×𝜋×40 = 80π cm

 Now, we find total distance covered

 We know that, Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/(𝑇𝑖𝑚𝑒 ) 

Here, Speed = 66 km/hr

 Time = 10 minutes = 10/60 hour = 1/6 hour 

Putting value in formula 66 = Distance/(1/6) 66 ×1/6 = Distance 11 = Distance Distance = 11 km 

Distance = 11 km = 11 × 1000 m = 11000 m = 11000 ×100 cm = 1100000 cm

 Now , 

Number of revolutions = (𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒)/(𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑 𝑖𝑛 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛) = 1100000/80π = 110000/8π = 110000/(8 × 22/7) = (110000 × 7)/(8 × 22) = 4375

 Hence, number of revolutions = 4375

QUESTION 5:Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is 

(A) 2 UNITS     (B)  𝜋 UNITS       ( C)   4 UNITS        (D)  7 UNITS

Answer

It is given that Perimeter = area of a circle

2 𝜋r =  πr²

^{=> 2r =} r²

^{=> r = 2 units}

 Hence A is correct.