Question

A conical paper cup is to have a height of 3 inches. Find the radius r of the cone that will result in a surface area of 6 in2.
r=

Answer 1

Answer:

The radius of the conical cup is 1.95 in.

Step-by-step explanation:

Given:

Height of the conical cup is $h=3$ inches.

Area or curved surface area of the cup is $A=6\rm{in^{2}}$

Let the radius of the cup is $r$.

Now, the lateral height $l$ of the cone will be,

$l=\sqrt{r^{2}+h^{2}}\\l=\sqrt{r^{2}+3^{2}}$

The curved surface area of the cone is,

$A=\pi rl\\6=\pi r \sqrt{r^{2}+9}\\r \sqrt{r^{2}+9}=1.91$

Squaring the both sides,

$r^{2} (r^{2}+9)=3.6$

Now, let $r^{2}=x$ and solve the resulting quadratic equation.

$x (x+9)=3.6\\x^{2}+9x-3.6=0$

Solving the above quadratic equation as,

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\\x=\frac{-9\pm \sqrt{9^{2}-4\times1\times(-3.6)}}{2\times9}\\x=0.38, -9.38$

Now, the value of $x$ cannot be negative as it is the square of radius.

So, the value of radius of the cone will be,

$r=\sqrt{x}\\r=\sqrt{0.38}\\r=1.95\rm{in}$

Therefore, the radius of the conical cup is 1.95 in.

For more details, refer the link,

https://brainly.com/question/12267785?referrer=searchResults