Chapter 12.3, Problem 34WE

a.

To determine

To determine the volume of the pyramid

Answer to Problem 34WE

The volume of the pyramid is $\frac{128}{3}$ $c{m}^3$

Explanation of Solution

Given: Consider thegiven information,

Radius of pyramid = 4cm

Height of pyramid = 4cm

Formula Used:

Volume of the pyramid = $a^2\frac{h}{3}$

Calculation: Let the edge of the base square = a

Then, $a^2+a^2={(2r)}^2$

  $2a^2=4r^2$

  $a=r\sqrt{2}$

Therefore, the volume of the pyramid = ${(r\sqrt{2})}^2\times \frac{4}{3}$ = $\frac{16\times 2\times 4}{3}$ = $\frac{128}{3}$ $c{m}^3$

Conclusion:

The volume of the pyramid is $\frac{128}{3}$ $c{m}^3$

b.

To determine

To determine the slant height of cone and pyramid

Answer to Problem 34WE

The slant height of cone and pyramid is $4\sqrt{2}$ cm

Explanation of Solution

Given:Consider thegiven information,

Radius of pyramid = 4cm

Height of pyramid = 4cm

Calculation:The slant height of the cone and the pyramid is,

Slant height = $\sqrt{{(4)}^2+{(4)}^2}$ = $4\sqrt{2}$ cm

Conclusion:

The slant height of cone and pyramid is $4\sqrt{2}$ cm