What is the whole surface area of a cone of base radius 7 cm and height 24 cm?

Options

A. 654 sq cm
B. 704 sq cm
C. 724 sq cm
D. 964 sq cm

Answer

To find the whole surface area of a cone, we need to follow these steps:

### Step 1: Identify the given values
- Base radius (r) = 7 cm
- Height (h) = 24 cm

### Step 2: Calculate the slant height (l)
The slant height of a cone can be calculated using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]

Substituting the values:
\[ l = \sqrt{(7 \, \text{cm})^2 + (24 \, \text{cm})^2} \]
\[ l = \sqrt{49 \, \text{cm}^2 + 576 \, \text{cm}^2} \]
\[ l = \sqrt{625 \, \text{cm}^2} \]
\[ l = 25 \, \text{cm} \]

### Step 3: Use the formula for the whole surface area of the cone
The whole surface area (A) of a cone is given by the formula:
\[ A = \pi r (r + l) \]

### Step 4: Substitute the values into the formula
Using \( \pi \approx 3.14 \):
\[ A = \pi \cdot 7 \, \text{cm} \cdot (7 \, \text{cm} + 25 \, \text{cm}) \]
\[ A = 3.14 \cdot 7 \, \text{cm} \cdot 32 \, \text{cm} \]

### Step 5: Calculate the area
\[ A = 3.14 \cdot 7 \cdot 32 \]
\[ A = 3.14 \cdot 224 \]
\[ A = 703.36 \, \text{cm}^2 \]

### Step 6: Round off the answer
The whole surface area of the cone is approximately:
\[ A \approx 704 \, \text{cm}^2 \]

### Final Answer
The whole surface area of the cone is **704 cm²**.

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