NCERT Solutions Maths Class 10 Exercise 12.1

Maths Class 10 Exercise 12.1

 

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.

Solution: Radius of the first circle = 19 cm

Circumference of the first circle = 2πr

                                                         = 2π × 19 = 38π cm

Radius of the second circle = 9 cm

Circumference of the second circle = 2πr

                                                               = 2π × 9 = 18π cm

According to question,

Circumference of the larger circle = Circumference of the first circle + Circumference of                             the second circle

Or, 2πr = 38π + 18π = 56π

Or, 2r = 56

Or, r = 28 cm

Hence, the radius of the larger circle is 28 cm.

 

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.

Solution: Radius of the first circle = 8 cm

Area of the first circle = πr²

                                       = π8²

                                       = 64π sq. cm

Radius of the second circle = 6 cm

Area of the second circle = π6²

                                             = 36π sq. cm

According to question,

Area of the larger circle = 64π + 36π

                                           = 100π sq. cm

Or, πr² = 100π

Or, r² = 100

Or, r = 10 cm

Hence, the radius of the larger circle is 10 cm.

 

3. Following figure depicts an archery target marked with its five scoring areas 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.

Solution: Area of Gold Region = πr²

                                                   = π10.5² = π110.25 = 346.5 sq. cm

Area of Red Region = π(r₁² – r₂²)

                                 = π(21² – 10.5²)

                                 = π(21 + 10.5)(21 – 10.5)

                                 = π × 31.5 × 10.5

                                 = 1039.5 sq. cm

Area of Blue Region = πr²

                                  = π(31.5² – 21²)

                                  = 1732.5 sq. cm

Area of Black Region = πr²

                                    = π(42² – 31.5²)

                                    = 2425.5 sq. cm

Area of White Region = πr²

                                     = π(52.5² – 42²)

                                     = 3118.5 sq. cm

 

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?

Solution: Speed of the car = 66 km/h

Distance covered by the car in 10 minutes = 66 km/h × (10/60) h = 11 km

Circumference of the wheel = πd = 80π

                                                      = 22/7 × 80 cm

Distance travelled by the car in 1 revolution = 22/7 × 80 cm

Therefore, the number of revolutions = (11 × 1000 × 100) ÷ (22/7 × 80)
                                                            = 4375

 

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

Solution: (A) 2 units

Because the perimeter of the circle = the area of the circle

Or, 2πr = πr²
Or, πr²/πr = 2

Or, r = 2 units