Question

Assertion: If the outer and inner diameters of a circular path are 10 m and 4 m, then the area of the path is 21π m².

Reason: Area of a circular path with radii R and r is given by π(R² – r²).

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Assertion: If the outer and inner diameters of a circular path are 10 m and 4 m, then the area of the path is 21π m².

Calculate the area of the circular path:

Outer radius R = `(10  m)/2` = 5 m

Inner radius r = `(4  m)/2` = 2 m

Area of the circular path = π(R² – r²) 

= π(5² – 2²) 

= π(25 – 4)

= 21π m²

The assertion is true.

Reason: Area of a circular path with radii R and r is given by π(R² – r²).

The reason is also true as it correctly states how to find the area of the circular path ring.

Since both assertion and reason are true and the reason correctly explains the assertion.