Question

Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for л. The surface area of the cone is about cm². (Round to the nearest whole number as needed.) 19 cm 4 cm (The figure is not drawn to scale.)​

Answer 1

The surface area of the cone rounded to the nearest whole number is; 346 cm²

How to determine the cone surface area?

We are given the parameters:

Radius; r = 5 cm

Slant height; l = 17 cm

The surface area is gotten from the formula;

A = πr(r +l)

Plug in the relevant values to get;

A = 3.14 × 5 × (5 + 17)

A = 345.5 square centimeters

Approximating to a whole number gives;

A = 346 square centimeters

Thus, the surface area of the cone is 346 square centimeters

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Answer 2

Answer:

  289 cm²

Step-by-step explanation:

The net for the surface area of a cone is a circular sector representing the lateral area, together with a circle representing the area of the base. The arc length of the sector is equal to the circumference of the base.

__

base area

The area of the circular base is given by the area formula for a circle:

  A = πr²

For the given radius, the area is ...

  A = (3.14)(4 cm)² = 50.24 cm²

lateral area

The circumference of the circular base is ...

  C = 2πr = 2(3.14)(4 cm) = 25.12 cm . . . . also the arc length of the sector

The area of the sector is ...

  A = 1/2hs . . . . where h is the radius of the sector, and s is its arc length

  A = (1/2)(19 cm)(25.12 cm) = 238.64 cm²

total surface area

The total surface area is the sum of the base area and the lateral area:

  SA = 50.24 cm² +238.64 cm² = 288.88 cm² ≈ 289 cm²

The surface area of the cone is about 289 cm².