Question

Find the total surface area of the following
cone. Leave your answer in terms of m.
12 cm
5 cm
Hint: Surface Area of a Cone = url + B
Where l = slant height, and B = area of the base
S.A. = [? ]n cm?

Answer 1

Answer:

$S.A.=90\pi~cm^2$

Step-by-step explanation:

Surface Area of a Cone

Given a cone of base area B and slant height L, the surface area can be calculated with the formula:

$S.A.=\pi rL +B$

The cone presented in the image has a circular base of radius r=5 cm, thus its base area is:

$B=\pi r^2$

$B=\pi 5^2$

$B=25\pi~cm^2$

The slant height can be calculated as the hypotenuse of a right triangle with legs 5 cm and 12 cm by using Pythatgora's Theorem:

$L^2=5^2+12^2$

$L^2=25+144=169$

Taking square roots

$L = \sqrt{169}$

L = 13 cm

The surface area is:

$S.A.=\pi (5~cm)*13~cm +25\pi~cm^2$

Operating:

$S.A.=65\pi~cm^2 +25\pi~cm^2$

$\mathbf{S.A.=90\pi~cm^2}$

Answer 2

Answer:

90

Step-by-step explanation: