# Video: Finding the Total Surface Area of a Cone given Its Slant Height and Base Radius

Determine, to the nearest hundredth, the total surface area of the cone shown.

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### Video Transcript

Determine to the nearest hundredth the total surface area of the cone shown.

First, letβs recall the formula for calculating the surface area of a cone. It is ππ squared plus πππ, where π represents the radius of the cone and π represents the slant height. The first term ππ squared gives the area of the circle on the base of the cone, the second term πππ gives the curved surface area of the cone, and together these give the total surface area.

Weβve been given the values of π and π in the diagram: π is 19 centimetres and π is 40 centimetres. Remember π represents the slant height of the cone, not the perpendicular height, and it is the slant height that weβve been given. So letβs substitute the values of π and π into our formula for the total surface area.

We have that the surface area is equal to π multiplied by 19 squared plus π multiplied by 19 multiplied by 40. Evaluating each of these constants gives 361 π plus 760 π. Combining these two terms gives a total surface area of 1121 π. The question remember has asked for the surface area to the nearest hundredth, so we need to evaluate this as a decimal and then round. The decimal is 3521.7253 and rounding this to the nearest hundredth will give us our answer: 3521.73, and the units of this surface area are centimetres squared.