Question

Which of the following statements are incorrect?(A) Volume of a cone = \(\frac{1}{3} \pi r^3 h\) (B) Volume of a cone = \(\frac{1}{3} \pi r^2 h\)  (C) Volume of a hemisphere = \(\frac{2}{3} \pi r^2\)  (D) Volume of a hemisphere = \(\frac{2}{3} \pi r^3\)  (E) Volume of a cylinder = \(\frac{1}{3} \pi r^3 h\)  Choose the correct answer from the options given below:

• A. Argument (A) and (B) are strong
• B. Only argument (A) is strong
• C. Argument (B) and (C) are strong
• D. Only argument (C) is strong

Answer 1

The Correct Option is B

To determine which statements are incorrect regarding the volume formulas, let's evaluate each one based on standard mathematical knowledge.

(A) Volume of a cone = \(\frac{1}{3} \pi r^3 h\)

(B) Volume of a cone = \(\frac{1}{3} \pi r^2 h\)

(C) Volume of a hemisphere = \(\frac{2}{3} \pi r^2\)

(D) Volume of a hemisphere = \(\frac{2}{3} \pi r^3\)

(E) Volume of a cylinder = \(\frac{1}{3} \pi r^3 h\)

Let's analyze each statement:

• For a cone, the correct volume formula is \(V = \frac{1}{3} \pi r^2 h\).
  • Statement (A) claims \(\frac{1}{3} \pi r^3 h\), which is incorrect as the \(r^3\) should be \(r^2\).
  • Statement (B) uses the correct formula, so it is correct.
• For a hemisphere, the correct volume formula is \(V = \frac{2}{3} \pi r^3\).
  • Statement (C) claims \(\frac{2}{3} \pi r^2\), which is incorrect. The power of \(r\) should be 3, not 2.
  • Statement (D) uses the correct formula for a hemisphere, so it is correct.
• For a cylinder, the correct volume formula is \(V = \pi r^2 h\).
  • Statement (E) claims \(\frac{1}{3} \pi r^3 h\), which resembles the incorrect cone formula and is therefore incorrect.

Conclusion: From the given options, the only statement identified as correct is statement (A), as options (B), (C), and (E) are incorrect. Therefore, the correct answer is Only argument (A) is strong.