Question

Need help with this last question. 98 points. Please explain how you got the answer. Thank you.

Answer 1

5m

Explanation:

2 pyramids are similar so all their dimensions are in the same ratio.

let that ratio be x

vol of smaller pyramid = 1/3*height*width*length

vol of larger pyramid = 1/3*(larger height)*(larger width)*(larger length)

= 1/3*(x*height)*(x*width)*(x*length)

= 1/3*height*width*length*x^3

= vol of smaller pyramid*x^3

substitute in the volume values

125 = 27*x^3

x^3 = 125/27

x = 5/3

height of larger pyramid = x*height of smaller pyramid

= 5/3*3

= 5m

Answer 2

The height of the large pyramid is 5m

Explanation:

V large pyramid = 125

V small pyramid 27

Vlarge/V small = 125/27

The scale factor with volume is as cubed so take the cubed root

(125/27) ^ (1/3) = 5/3

The scale factor is 5/3

Large over small is as 5/3

The height of the small pyramid is 3 m. I will use proportions putting the large on the top and the small on the bottom. h is the height of the large pyramide

5 h

----- = ---------

3 3 m

Using cross products

3*5 = 3h

Divide by 3

3*5/3 = 3h/3

5 =h