The surface are of a cone with radius r units and slant height s units is shown below: Surface area = 3.14(rs + r^2)

Part A: If r = 3 units and s = 5 units, write and expression that can be used to calculate the surface area of the cone. (4 points)

Part B: What is the surface area of the cone? Show your work. (6 points)

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Part A

The expression that can be used to calculate the surface area of the cone,  is;

Surface area ≈ 3.14 × (3 units  × 5 units + (3 units)²)

Part B

The surface area of the cone is 75.36 units²

Step-by-step explanation:

The surface area, 'SA', of a cone is given by the following formula;

SA = π·r·s + π·r² = π·(r·s + r²)

Where;

s = The slant height of the cone

r = The radius of the cone

π ≈ 3.14

∴ The surface area of the cone, SA ≈ 3.14·(r·s + r²)

Part A

If r = 3 units, and s = 5 units, by plugging in the values in the formula for SA, we have;

SA ≈ 3.14·(r·s + r²) = 3.14 × (3 units  × 5 units + (3 units)²)

Therefore, the expression that can be used to calculate the surface area of the cone, SA, is presented as follows;

Surface area ≈ 3.14 × (3 units  × 5 units + (3 units)²)

Part B

The surface area is found by evaluating the expression above that can be used to calculate the surface area of the cone as follows;

SA ≈ 3.14 × (3 units  × 5 units + (3 units)²)  = 3.14 × (15 units² + 9 units²)

∴ SA ≈  3.14 × 24 units² = 75.36 units²

The surface area, SA ≈ 75.36 units²

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