Chapter 12.5, Problem 10PSB

a.

To determine

To find: The coordinates of point C in a regular square pyramid PABCD .

Answer to Problem 10PSB

The coordinates of point Care $\left(0,10,0\right)$ .

Explanation of Solution

Given information:

PABCD is a regular square pyramid.

The coordinates of point Pare $\left(5,5,12\right)$ .

Calculation:

  

PABCD is a regular pyramid and coordinates of point Pare $\left(5,5,12\right)$ .

The point C lies on y - axis. Its x and y coordinates are 0.

Point P is equidistant from points D and C.

The coordinates of point Pare $\left(5,5,12\right)$ , point C must be 5 + 5 along the y -axis.

The coordinates of point Care $\left(0,10,0\right)$ .

b.

To determine

To calculate: The volume of a pyramid PABCD .

Answer to Problem 10PSB

The volume of a pyramid PABCD is $400$ .

Explanation of Solution

Given information:

PABCD is a regular square pyramid.

The coordinates of point Pare $\left(5,5,12\right)$ .

Formula used:

Volume of pyramid $=\frac{1}{3}B\times h$

B = Base area of pyramid and h = height of pyramid

Area of square: $A=s^2$

s = side of square

Calculation:

  

PABCD is a regular pyramid and coordinates of point Pare $\left(5,5,12\right)$ .

The point C lies on y - axis. Its x and z coordinates are 0.

Point P is equidistant from points D and C.

The coordinates of point Pare $\left(5,5,12\right)$ , point C must be 5 + 5 along the y -axis.

The coordinates of point Care $\left(0,10,0\right)$ .

Side DC = 10

Base area of pyramid:

  $B={\left(10\right)}^2=100$

The height of pyramid is the z coordinate of point P.

  $\begin{array}{l}h=12\\ V_{Pyramid}=\frac{1}{3}\times B\times h\\ V_{Pyramid}=\frac{1}{3}\times \left(100\right)\times 12\\ V_{Pyramid}=400\end{array}$