curved surface area of a cone $$ =\pi r l $$, where $$ r $$ is the radius and $$ l $$ is the slant height. A frustum is formed by removing a small cone from a similar, larger cone, as shown below. a) Work out, in terms of $$ \pi $$, the curved surface area of the frustum. b) Work out, in terms of $$ \pi $$, the total surface area of the frustum.

Question

UpStudy AI · Accepted Answer

a) The curved surface area of the frustum can be calculated by subtracting the curved surface area of the small cone from the curved surface area of the large cone.

Given:
- Curved surface area of a cone = $$ \pi r l $$
- Let $$ r_1 $$ be the radius of the small cone and $$ l_1 $$ be the slant height of the small cone.
- Let $$ r_2 $$ be the radius of the large cone and $$ l_2 $$ be the slant height of the large cone.

The curved surface area of the frustum is:
$$ \text{Curved surface area of frustum} = \pi r_2 l_2 - \pi r_1 l_1 $$

b) To find the total surface area of the frustum, we need to add the curved surface area of the frustum to the areas of the two bases of the frustum.

The total surface area of the frustum is:
$$ \text{Total surface area of frustum} = \text{Curved surface area of frustum} + \text{Area of base of large cone} + \text{Area of base of small cone} $$

Let's calculate the total surface area of the frustum.
Simplify the expression by following steps:
- step0: Solution:
  $$\pi r_{2}l_{2}-\pi r_{1}l_{1}$$
The curved surface area of the frustum is $$ \pi r_2 l_2 - \pi r_1 l_1 $$.

Now, let's calculate the total surface area of the frustum.
Simplify the expression by following steps:
- step0: Solution:
  $$\pi r_{2}l_{2}-\pi r_{1}l_{1}+\pi r_{2}^{2}+\pi r_{1}^{2}$$
The total surface area of the frustum is $$ \pi r_2 l_2 - \pi r_1 l_1 + \pi r_2^2 + \pi r_1^2 $$.
a) The curved surface area of the frustum is $$ \pi r_2 l_2 - \pi r_1 l_1 $$. b) The total surface area of the frustum is $$ \pi r_2 l_2 - \pi r_1 l_1 + \pi r_2^2 + \pi r_1^2 $$.

curved surface area of a cone ,
where is the radius and is the slant
height.
A frustum is formed by removing a
small cone from a similar, larger cone,
as shown below.
a) Work out, in terms of , the curved
surface area of the frustum.
b) Work out, in terms of , the total
surface area of the frustum.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Geometry Questions

curved surface area of a cone , where is the radius and is the slant height. A frustum is formed by removing a small cone from a similar, larger cone, as shown below. a) Work out, in terms of , the curved surface area of the frustum. b) Work out, in terms of , the total surface area of the frustum.