Circumference & Area of a Circle — Assertion-Reason Type Questions

Assertion (A): Total surface area of semi-circle is 18.48 cm². Its radius is 14 cm.

Reason (R): Total surface area of a semi-circle of radius r is given by 2πr².

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

Total surface area of semicircle formula = $\dfrac{1}{2}πr^2$

Considering radius = 14 cm

Total surface area of semicircle = $\dfrac{1}{2} × \dfrac{22}{7}$ × 14²

= 308 cm².

But the given assertion says 18.48 cm².

∴ Both Assertion and Reason are false.

Hence, option 4 is the correct option.

Assertion (A): The diameter of a cycle wheel is 21 cm. It will make 2000 revolutions to cover a distance of 1.32 km.

Reason (R): Distance covered by a wheel of radius r in one revolution is given by 2πr.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

Diameter of wheel = 21 cm

Distance covered in 1 revolution = Circumference of the wheel = 2πr

∴ Reason (R) is true.

We know that,

Circumference of wheel = 2πr = πd

= $\dfrac{22}{7}$ × 21

= 66 cm.

Distance covered in 2000 revolutions

= 2000 × 66 = 132000 cm = $\dfrac{132000}{100000}$ = 1.32 km

∴ Assertion (A) is true.

Both Assertion and Reason are true.

Hence, option 3 is the correct option.