Question

The square pyramid has a volume of 441 cubic inches. What is the value of x?

1/7x is the height


x is the base

Answer 1

Answer:

x = 96.23   if  x is the area of the base

x =21          if x is the side length of the base

Step-by-step explanation:

The volume of a square pyramid is given by

V=1/3 a^ 2 h

We know the volume is 441 and the area of the base is a^2 which is x

and the height is 1/7x

Substituting these values in

441 = 1/3 (x) 1/7x

441 =1/21 x^2

Multiply each side by 21

441*21 = 21*1/21 x^2

9261 = x^2

Take the square root of each side

sqrt(9261) = sqrt(x^2)

x = 96.23

I am thinking you mean x is the side length on the base

We know the volume is 441 and the area of the base is a^2 which is x^2

and the height is 1/7x

Substituting these values in

441 = 1/3 (x^2) 1/7x

441 =1/21 x^3

Multiply each side by 21

441*21 = 21*1/21 x^3

9261 = x^3

Take the cube root of each side

(9261) ^ (1/3) = (x^3)^(1/3)

21 =x

Answer 2

Answer:

x = 21

Step-by-step explanation:

The formula of a volume of a square pyramid:

$V=\dfrac{1}{3}a^2H$

a - edge of base

H - height

We have

$V=441\ in^3,\ a=x,\ H=\dfrac{1}{7}x$

Substitute:

$\dfrac{1}{3}x^2\left(\dfrac{1}{7}x\right)=441\\\\\dfrac{1}{21}x^3=441\qquad\text{multiply both sides by 21}\\\\x^3=9,261\to x=\sqrt[3]{9,261}$

Use calculator:

$\sqrt[3]{9,261}=21$

or

$\begin{array}{c|c}9,261&3\\3,087&3\\1,029&3\\343&7\\49&7\\7&7\\1\end{array}\\\\9,261=3^3\cdot7^3\\\\\sqrt[3]{9,261}=\sqrt[3]{3^3\cdot7^3}=\sqrt[3]{3^3}\cdot\sqrt[3]{7^3}=3\cdot7=21$