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Calculate the total surface area of a cone with a base radius of 5 cm and a slant height of 12 cm.

May 20, 2026Mathematics

ScanSolve AI Answer

Answer

85\pi \text{ cm}^2

267.04 \text{ cm}^2

4 steps

Identify the given values.
The radius of the base is $r = 5 \text{ cm}$ .
The slant height is $l = 12 \text{ cm}$ .
Write down the formula for the total surface area of a cone.
The total surface area (TSA) of a cone is given by the formula:
$TSA = \pi r (r+l)$
Substitute the given values into the formula.
Substitute $r = 5 \text{ cm}$ and $l = 12 \text{ cm}$ into the formula:
$TSA = \pi (5 \text{ cm}) (5 \text{ cm} + 12 \text{ cm})$
Calculate the total surface area.
$TSA = \pi (5 \text{ cm}) (17 \text{ cm})$ $TSA = 85\pi \text{ cm}^2$
If we use $\pi \approx 3.14159$ :
$TSA \approx 85 \times 3.14159 \text{ cm}^2$ $TSA \approx 267.03515 \text{ cm}^2$
The total surface area of the cone is $\boxed{85\pi \text{ cm}^2}$ or approximately $\boxed{267.04 \text{ cm}^2}$ .