Question

22cm d=25cm what is the surface of the cone use 3.14 for pi

Answer 1

To find the surface area of a cone, you need to know the radius (r), the height (h), and the slant height (l) of the cone. The formula for the total surface area (A) of a cone is:

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

Given the diameter (d) of the base of the cone is 25 cm, the radius (r) can be computed as follows:

\[
r = \frac{d}{2} = \frac{25}{2} = 12.5 \text{ cm}
\]

You also provided the height (h) of the cone, which is 22 cm. To find the slant height (l), we can use the Pythagorean theorem:

\[
l = \sqrt{r^2 + h^2}
\]
\[
l = \sqrt{(12.5)^2 + (22)^2}
\]
\[
l = \sqrt{156.25 + 484}
\]
\[
l = \sqrt{640.25} \approx 25.3 \text{ cm} \quad (\text{rounded to one decimal place})
\]

Now we can substitute the values of \( \pi \), \( r \), and \( l \) into the surface area formula:

\[
A = \pi r (r + l)
\]
\[
A = 3.14 \times 12.5 \times (12.5 + 25.3)
\]
\[
A = 3.14 \times 12.5 \times 37.8
\]
\[
A \approx 3.14 \times 12.5 \times 37.8 \approx 1481.925 \text{ cm}^2 \quad (\text{rounded to three decimal places})
\]

Therefore, the surface area of the cone is approximately \( 1481.93 \text{ cm}^2 \).