Question

Find the lateral area of the cone holding french fries. The diameter is 10cm and the height is 15 cm. Round to the nearest whole number.

236
283
150
248

Answer 1

To find the lateral area (or lateral surface area) of a cone, we can use the formula:

\[
L = \pi r l
\]

where \( r \) is the radius of the base of the cone, \( l \) is the slant height, and \( \pi \) is approximately 3.14.

First, we need to calculate the radius \( r \) from the diameter:

\[
r = \frac{diameter}{2} = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm}
\]

Next, we need to calculate the slant height \( l \) of the cone. We can find \( l \) using the Pythagorean theorem:

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

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

\[
h = 15 \, \text{cm}
\]

Calculating \( l \):

\[
l = \sqrt{5^2 + 15^2} = \sqrt{25 + 225} = \sqrt{250} = 5\sqrt{10} \approx 15.81 \, \text{cm}
\]

Now, we can calculate the lateral area \( L \):

\[
L = \pi r l \approx 3.14 \times 5 \times 15.81
\]

Calculating it:

\[
L \approx 3.14 \times 5 \times 15.81 = 3.14 \times 79.05 \approx 248.05 \, \text{cm}^2
\]

Rounding to the nearest whole number, we find:

\[
L \approx 248 \, \text{cm}^2
\]

Thus, the lateral area of the cone is \( \boxed{248} \).