Question

Apyramid has volume of 32cm3 evertical height

8cm. Asimilar pyramid has volume 16 384 cm.
What is its vertical height?

Answer 1

64cm

Explanation:

(Side1/Side2)³ = Volume1/Volume2

(H/8)³ =

H³/256 = 16384/32

H³ = 262144

H = 64cm

Answer 2

64 cm

Explanation:

Given 2 similar figures with linear ratio = a : b, then

ratio of volumes = a³ : b³

Given

ratio of volume = 32 : 16384 then

ratio of heights =
`\sqrt[3]{32}` :
`\sqrt[3]{16384}` ← values are not exact cubes

Using proportion then letting x be height of larger pyramid

`\frac{\sqrt[3]{16384} }{\sqrt[3]{32} }` =
`(x)/(8)`, that is

8 =
`(x)/(8)` ( multiply both sides by 8 )

64 = x

That is vertical height is 64 cm