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. (A), (B), and (D) only
• B. (A), (B), and (C) only
• C. (A), (C), and (E) only
• D. (C), (D), and (E) only

Answer 1

The Correct Option is C

To determine which statements are incorrect, we need to know the correct formulas for the volumes of different geometric shapes:

• The volume of a cone is given by: \( V = \frac{1}{3} \pi r^2 h \).
• The volume of a hemisphere is given by: \( V = \frac{2}{3} \pi r^3 \).
• The volume of a cylinder is given by: \( V = \pi r^2 h \).

Now, let's evaluate the provided statements:

1. (A) Volume of a cone = \(\frac{1}{3} \pi r^3 h\):
   The correct formula is \(\frac{1}{3} \pi r^2 h\), so this statement is incorrect.
2. (B) Volume of a cone = \(\frac{1}{3} \pi r^2 h\):
   This matches the correct formula, so this statement is correct.
3. (C) Volume of a hemisphere = \(\frac{2}{3} \pi r^2\):
   The correct formula is \(\frac{2}{3} \pi r^3\), so this statement is incorrect.
4. (D) Volume of a hemisphere = \(\frac{2}{3} \pi r^3\):
   This matches the correct formula, so this statement is correct.
5. (E) Volume of a cylinder = \(\frac{1}{3} \pi r^3 h\):
   The correct formula is \(\pi r^2 h\), so this statement is incorrect.

Based on above evaluation, the incorrect statements are (A), (C), and (E). Therefore, the correct option is:

(A), (C), and (E) only