Chapter 10.3, Problem 71E

To determine

To find the radius of each cone

Answer to Problem 71E

Radius of cone A is 2 units.

Radius of cone A is 4 units.

Explanation of Solution

Given information:

  $s=\sqrt{r^2+h^2}$

Calculation:

Height of cone A is 4, radius is r .

Height cone of B is 2, radius is 2r .

Slant height of cone A= $\sqrt{r^2+4^2}$

Slant height of cone B= $\sqrt{{(2r)}^2+{(2)}^2}$

According to question, slant height of cones are same.

So,

  $\sqrt{{(2r)}^2+{(2)}^2}=\sqrt{r^2+4^2}$

Squaring both sides,

  ${(\sqrt{{(2r)}^2+{(2)}^2})}^2={(\sqrt{r^2+4^2})}^2$

Solving,

  ${(2r)}^2+{(2)}^2=r^2+4^2$

So,

  $4r^2+4=r^2+16$

Now adding like terms,

  $4r^2-r^2=+16-4$

Dividing equation by 3,

  $r^2=\frac{12}{3}$

So,

  $r^2=4$

Rooting both sides,

  $r=2$

Hence, radius of cone A is 2units.

Radius of cone B= 2r = 2(2) = 4 units.