Question

A rectangular pyramid has a base with dimensions 5 inches by 7 inches. The height of the pyramid is unknown. If the volume of the pyramid is 105 cubic inches, what is the height of the pyramid? Explain the steps.

Answer 1

To find for the height of the rectangular pyramid with base whose dimensions are 5 inches and 7 inches, use the formula V = 1/3 Bh where, B is l x w such that V = 1/3Bh

      105 inches^3 = 1/3 (5 inches)(7 inches) h

      105 inches^3 = 1/3 (35 inches^2) h

      105 inches^3 = 35 inches^2h

                                       3

    3(105 inches^3 = 35 inches^2h)3

                                        3

      315 inches^3 = 35 inches^2h

         35 inches^2   35 inches^2

           9 inches    = h

Therefore, the height of the rectangular pyramid is 9 inches.

Answer 2

height of the pyramid when volume is 105 inch³,base length and width as 5 and 7 inches is

9 inches

Step-by-step explanation:

given that here,

length and breath of the base are 5 and 7

volume/=105

Then,

to solve for the height of the pyramid,

$h = 3 \frac{v}{lw}$

substituting the given values of pyramid in the above equation we have

$\\ h = 3 \frac{105}{5 \times 7}$

simplifying we have the value of h as,

$\\ h = 3 \times 3 = 9$

DEFINITIONS

• RECTANGULAR PYRAMID

A three dimensional geometrical figure made with 3 triangle as lateral sides and base as a rectangle

• if base is a square it is a square pyramid, if it's base is a pentagon then pentagonal pyramid .etc.

• EQUATION FOR THE VOLUME OF A RECTANGULAR PYRAMID

$v = \frac{lwh}{3} \\ h = 3 \frac{v}{lw}$

were,

v=volume of the pyramid

w=width of base rectangle

l=length of base rectangle

h=height of the pyramid

some more related questions to refer

the base of a pyramidal tent is square.If the tent is 2m long and 3m high,how many cubic meter of space can it hold insi

https://brainly.in/question/40253105

draw a rough diagram of Square pyramid

https://brainly.in/question/8897653

#spj3