Question

Find the following, giving your answers

Answer 1

Answer:

  a) 301.6 cm³

  b) 188.5 cm²

Step-by-step explanation:

The volume and lateral surface area of the cone can be found using the given dimensions with the given formulas. All that is needed is to substitute the appropriate values and do the arithmetic.

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a) volume

The volume is given by the formula ...

  V = 1/3πr²h

The dimensions are given on the diagram: r = 6 cm, h = 8 cm. Using these values in the formula, we find the volume to be ...

  V = 1/3π(6 cm)²(8 cm) = 96π cm³ ≈ 301.6 cm³

The volume of the cone is about 301.6 cm³.

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b) area

The lateral area of the cone is given by the formula ...

  A = πrl

The dimensions are given on the diagram: r = 6 cm, l = 10 cm (the slant height). Using these values in the formula, we find the area to be ...

  A = π(6 cm)(10 cm) = 60π cm² ≈ 188.5 cm²

The area of the curved surface is about 188.5 cm².