area of lateral surface

Question

The circumference of the base of a right circular cone is 41.6 in., and the slant height is 40.0 in. What is the area of the lateral surface? Round the answer to the nearest integer.

Answer 1

Hello Sara, without an h

 

To solve this problem all you have to do is plug the number into the formula for the Lateral Surface Area of a Cone

 

LSA= (Pi)(radius)(slant height)

I am going to use 3.14 for Pi, and we are told that the slant height is 40. So all we are missing is the radius.  The radius can be found by dividing the circumference of a circle by 6.28.  This is why.

 

Circumference = 2 (Pi) (radius)

(circumference)/ (2)(Pi) = radius

If we use 3.14 for Pi, we get 2Pi = 6.28

So, for this problem the circumference is 41.6, that means that its radius must be. (41.6)/(6.28) = 6.62

 

So, to find the lateral surface area use the above formula,

(Pi)(radius)(slant height)

(3.14)(6.62)(40)= 832

 

I hope this can help you out.

D.Y. Taylor

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Answer 2

The circumference of the circle is 41.6 in., so in order to find the radius we do:

 

C = 2πr

41.6 = 2πr

6.62 = r

 

So now we have the radius of the circular base.

 

Now, the slant height of the cone is 40 in. The radius that we have found can be treated as one leg of a right triangle, and the slant height can be treated as the hypotenuse. We can then plug in those terms into the Pythagorean Theorem to find the altitude of the cone:

 

a² + b² = c²

6.62² + b² = 40²

43.8 + b² = 1600

b² = 1556.2

b = 39.45

 

The lateral surface area is the triangle that can be seen when a plane is cut through the top of the cone. The area would be:

 

A = (1/2)bh

A = (1/2)(2 x 6.62)(39.45)

A = 261.2

Answer 3

Area of Lateral Surface = pi*radius*(slant height)

 

We know the value of pi, and the slant height is 40 inches; so we need to find the radius of the base.  The circumference of the base is 41.6 inches.  The formula for the circumference is:

 

Circumference = 2*pi*radius

 

41.6 = 2*pi*radius

 

20.8/pi = radius

 

Now we have what we need:

 

Area of Lateral Surface = pi*radius*(slant height)

 

= pi*(20.8/pi)*(40)

 

= 20.8 * 40

 

= 832 in²