Question

calculate the total surface area of conical solid whose radius is 3.5cm and height 15cm

Answer 1

To find the total surface area of a cone, you can use the formula:

\[
\text{Total Surface Area} = \pi r (r + l)
\]

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

First, we need to calculate the slant height (\( l \)) using the Pythagorean theorem, which states:

\[
l = \sqrt{r^2 + h^2}
\]

where \( h \) is the height of the cone.

Given:
- \( r = 3.5 \, \text{cm} \)
- \( h = 15 \, \text{cm} \)

Now, we can compute \( l \):

\[
l = \sqrt{(3.5)^2 + (15)^2}
\]
\[
l = \sqrt{12.25 + 225}
\]
\[
l = \sqrt{237.25}
\]
\[
l \approx 15.4 \, \text{cm} \, (\text{rounded to one decimal place})
\]

Next, we substitute \( r \) and \( l \) into the total surface area formula:

\[
\text{Total Surface Area} = \pi \times 3.5 \times (3.5 + 15.4)
\]
\[
= \pi \times 3.5 \times 18.9
\]
\[
\approx 3.14 \times 3.5 \times 18.9
\]

Calculating the product:

\[
3.5 \times 18.9 \approx 66.15
\]
\[
\text{Total Surface Area} \approx 3.14 \times 66.15 \approx 207.23 \, \text{cm}^2
\]

Thus, the total surface area of the conical solid is approximately \( 207.23 \, \text{cm}^2 \).