Question

Assertion (A): A hemispherical bowl is made of steel of thickness 1 cm. If the inner radius of the bowl is 5 cm then the volume of steel used is $$\left(\frac{182}{3}\pi\right)\ \mathrm{cm}^{3}$$.

Reason (R): The volume of steel is calculated as the difference between the volumes of two hemispheres with radii 6 cm and 5 cm.

विकल्प

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The outer radius is $$5 + 1 = 6\ \mathrm{cm}$$. The volume of steel is: $$V = \frac{2}{3}\pi(6^{3} - 5^{3})$$ $$V = \frac{2}{3}\pi(216 - 125) = \frac{182}{3}\pi\ \mathrm{cm}^{3}$$

Step 2 – Reason: R is true. The steel occupies the region between the outer and inner hemispheres, so its volume is their volume difference.

Step 3 – Link: Applying the difference-of-hemispheres method with radii 6 cm and 5 cm gives exactly the assertion; R correctly explains A.