Question

A company makes candles in the shape of a right cone. The lateral surface of each candle is covered with paper for shipping and each candle also has a plastic circular base. Find the amount of paper needed to cover the lateral surface of each candle. Then find the total amount of paper and plastic needed for the candle. Round to the nearest tenth. Use 3.14 for π.

Answer 1

If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.

Explanation:

The question is incomplete: no numerical values for the dimensions of the cone are given.

A right cone is defined by the radius r of the base and the height h.

The base area is the area of a circle with radius r:

`A_b=\pi r^2`

The lateral area is calculated as:

`A_l=\pi \cdot r\cdot l`

As the values for r and h are not given, we will use an example with r=2 and h=3.

Then, the amount of paper needed is:

`A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2`

The amount of plastic needed is:

`A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2`