p : If a cylinder is right circular cylinder then its volume is `1/3pir^2h`
Contrapositive of statement p is

Options

A. If the volume of a cylinder is `1/3pir^2h` then it is right circular cylinde
B. If the volume of a cylinder is not `1/3pir^2h` then 3 it is nor right circular cylinder
C. If a cylinder is not right circular cylinder then its volume is not `1/3pir^2h`
D. Volume can't be `1/3pir^2h`

Answer

To find the contrapositive of the statement \( p \): "If a cylinder is a right circular cylinder, then its volume is \( \frac{1}{3} \pi r^2 h \)", we will follow these steps:

### Step 1: Identify the components of the statement
The statement can be broken down into:
- \( P \): "A cylinder is a right circular cylinder."
- \( Q \): "Its volume is \( \frac{1}{3} \pi r^2 h \)."

### Step 2: Write the implication
The original statement can be expressed in implication form as:
\[ P \implies Q \]
This means "If \( P \) is true, then \( Q \) is also true."

### Step 3: Formulate the contrapositive
The contrapositive of an implication \( P \implies Q \) is given by:
\[ \neg Q \implies \neg P \]
Where \( \neg Q \) is the negation of \( Q \) and \( \neg P \) is the negation of \( P \).

### Step 4: Determine the negations
- The negation of \( Q \) ("Its volume is \( \frac{1}{3} \pi r^2 h \)") is:
- "Its volume is not \( \frac{1}{3} \pi r^2 h \)" or simply "The volume of the cylinder is not \( \frac{1}{3} \pi r^2 h \)."

- The negation of \( P \) ("A cylinder is a right circular cylinder") is:
- "A cylinder is not a right circular cylinder."

### Step 5: Combine the negations into the contrapositive
Thus, the contrapositive statement becomes:
"If the volume of the cylinder is not \( \frac{1}{3} \pi r^2 h \), then the cylinder is not a right circular cylinder."

### Final Answer
The contrapositive of the statement \( p \) is:
"If the volume of the cylinder is not \( \frac{1}{3} \pi r^2 h \), then the cylinder is not a right circular cylinder."

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