Chapter 12, Problem 20PT

a.

To determine

To find the lateral surface area of the given cone.

Answer to Problem 20PT

Lateral surface $=298$ square centimeters

Explanation of Solution

Given:

  

A traffic cone

Radius, $(r)=5$ inches

Height,( $h$ ) $=19$ inches

Formula used:

Lateral surface area of a cone $=\pi rl$

where $r$ is the radius and $l$ is the slant height of the cylinder.

Pythagoras theorem:

In $\Delta ABC$ right angled at $B$ , then

  $A{B}^2+B{C}^2=C{A}^2$

Calculation:

  

In $\Delta ABC$,$A{B}^2+B{C}^2=C{A}^2$

Putting the values,

  $\Rightarrow {19}^2+5^2=C{A}^2$

  $\Rightarrow 361+25=C{A}^2$

  $\Rightarrow C{A}^2=386$

Taking square root on both sides,

  $\Rightarrow CA=l=19$ , where $l$ is the slant height of the cone.

To find the lateral surface area of the cone, use the following formula.

Lateral surface area $=\pi rl$

Now putting the values,

  $\Rightarrow 3.14\times 5\times 19$

  $\Rightarrow 298$ square inches

The lateral surface area of the cone is 298 square inches

Conclusion:

Hence, the lateral surface area is 298 square inches.

b.

To determine

To find the surface area of the given cone.

Answer to Problem 20PT

376 square inches

Explanation of Solution

Given:

  

A traffic cone

Radius, $(r)=5$ inches

Slant height,( $l$ ) $=19$ inches

Formula used:

Total surface area of a cone $=\pi r(l+r)$

where $r$ is the radius and $l$ is the slant height of the cylinder.

Calculation:

To find the surface area of the cone, use the following formula.

Lateral surface area $=\pi r(l+r)$

Now putting the values,

  $\Rightarrow 3.14\times 5\times (19+5)$

  $\Rightarrow 3.14\times 5\times 24$

  $\Rightarrow 376$ square inches

So, the surface area of the cone is 376 square inches.

Conclusion:

Therefore, the surface area of the cone is 376 square inches.