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The following formula is for the area, A, of the curved surface area of a cone - OCR - GCSE Maths - Question 15 - 2017 - Paper 1

Question 15

The following formula is for the area, A, of the curved surface area of a cone. A = πrl, where r is the radius and l is the slant height of the cone. Calculate the ... show full transcript

Worked Solution & Example Answer:The following formula is for the area, A, of the curved surface area of a cone - OCR - GCSE Maths - Question 15 - 2017 - Paper 1

Step 1

Calculate the curved surface area

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Answer

To find the curved surface area (A) of the cone, we use the formula:

$A = \pi rl$

where r = 5 cm and l = 12 cm.

Substituting the values:

$A = \pi (5)(12) = 60\pi \approx 188.5 \: cm^2$

Step 2

Calculate the base area

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Answer

The base area (B) of the cone is calculated using the formula for the area of a circle:

$B = \pi r^2$

where r = 5 cm.

Substituting the value:

$B = \pi (5)^2 = 25\pi \approx 78.5 \: cm^2$

Step 3

Calculate the total surface area

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Answer

The total surface area (S) of the cone is the sum of the curved surface area and the base area:

$S = A + B$

Substituting the values:

$S = 60\pi + 25\pi = 85\pi \approx 267.0 \: cm^2$

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