The surface area of a cone whose height is 10 cm and diameter is 8cm is

To find the surface area of a cone, we use the formula:

\[
A = \pi r (r + l)
\]

Where:
- \( r \) is the radius of the base,
- \( l \) is the slant height of the cone,
- \( h \) is the vertical height.

We are given:
- Height (\( h \)) = 10 cm,
- Diameter = 8 cm, so the radius (\( r \)) = 4 cm.

### Step 1: Find the slant height (\( l \))
Using the Pythagorean theorem, we can find the slant height as:

\[
l = \sqrt{r^2 + h^2}
\]
\[
l = \sqrt{4^2 + 10^2} = \sqrt{16 + 100} = \sqrt{116} \approx 10.77 \, \text{cm}
\]

### Step 2: Calculate the surface area
Now, using the surface area formula:

\[
A = \pi r (r + l)
\]
\[
A = \pi \times 4 \times (4 + 10.77) = \pi \times 4 \times 14.77 \approx 3.1416 \times 4 \times 14.77
\]
\[
A \approx 3.1416 \times 59.08 \approx 185.66 \, \text{cm}^2
\]

Thus, the surface area of the cone is approximately **185.66 cm²**.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the surface area change if the height was doubled but the diameter remained the same?
2. What is the volume of this cone using the same dimensions?
3. How would the surface area formula change if the cone had no base (open cone)?
4. What happens to the surface area if both the height and diameter are doubled?
5. How would you calculate the lateral surface area of the cone (without the base)?

**Tip:** When solving for surface area or volume, always double-check units and be clear about whether you're dealing with lateral surface area or total surface area.

The surface area of a cone whose height is 10 cm and diameter is 8 cm is

Learn how to calculate the surface area of a cone with a height of 10 cm and a diameter of 8 cm. This detailed solution walks through using the Pythagorean theorem and the surface area formula. Perfect for students in Grades 8-10 exploring geometry concepts.

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