We are asked to find the lateral area ($L$) and surface area ($S$) of a cone, given its diameter and slant height. The diameter is 3.4 cm and the slant height is 6.5 cm. We need to round our answers to the nearest tenth.

1. Problem Description

We are asked to find the lateral area ($L$) and surface area ($S$) of a cone, given its diameter and slant height. The diameter is 3.4 cm and the slant height is 6.5 cm. We need to round our answers to the nearest tenth.

2. Solution Steps

First, we need to find the radius $r$ of the cone. Since the diameter is 3.4 cm, the radius is half of the diameter:

$r = \frac{3.4}{2} = 1.7$ cm.

The formula for the lateral area $L$ of a cone is given by:

$L = \pi r l$,

where $r$ is the radius and $l$ is the slant height.

Substituting the given values, we have:

$L = \pi (1.7)(6.5) = 11.05 \pi \approx 34.714$

Rounding to the nearest tenth, we get $L \approx 34.7$ cm$^2$.

The formula for the surface area $S$ of a cone is given by:

$S = \pi r l + \pi r^2$,

where $r$ is the radius and $l$ is the slant height.

We already have the lateral area $L = \pi r l$, so $S = L + \pi r^2$.

Substituting the values, we get:

$S = 34.714 + \pi (1.7)^2 = 34.714 + \pi (2.89) = 34.714 + 9.079 \approx 43.793$

Rounding to the nearest tenth, we get $S \approx 43.8$ cm$^2$.

3. Final Answer

$L \approx 34.7$ cm$^2$

$S \approx 43.8$ cm$^2$