Kasey119
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A mute for a brass instrument is formed by taking a solid cone with a radius of 10 centimeters and an altitude of 20 centimeters and cutting off the top. The cut is made along a plane that is perpendicular to the altitude of the cone and intersects the altitude 6 centimeters from the vertex. Round your answers to the nearest hundredth.

What is the surface area of the original cone?
What is the surface area of the cone that is removed?
What is the surface area of the mute?

Respuesta :

facundo3141592

By using the formula for the area of a cone, we will get:

  • i)  942 cm^2
  • ii)  84.78cm^2
  • iii)  885.48cm^2

How to get the surface areas?

First, let's find the area of the original cone. Remember that for a cone of radius R and height H, the surface area is:

A  = pi*R^2 + pi*R*H

Then for the original cone where:

R = 10cm

H = 20cm

The area is:

A = 3.14*(10cm)^2 + 3.14*10cm*20cm = 942 cm^2

Now, we remove a smaller cone at 6 cm from the vertex, so we are removing a cone with height of 6 cm, and the radius of this cone is given by:

R' = R*(H'/H) = 10cm*(6cm/20cm) = 3cm

So the area of the removed cone is:

A' = 3.14*( (3cm)^2 + 3cm*6cm) = 84.78cm^2

The final area of the mute will be equal to the difference between the area of the original cone and the area of the removed cone, plus the area of the top cross-section (a circle of radius of 3cm)

A'' = 942 cm^2 - 84.78cm^2 + 3.14*(3cm)^2 = 885.48cm^2

If you want to learn more about areas, you can read

https://brainly.com/question/6613758

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