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A pyramid has a square base of side 4 cm and a volume of 16 cm3. Calculate:

A) the height of the pyramid
B) the height and the length of the side of the base of a similar pyramid with a volume
of 1024 cm3.

A pyramid has a square base of side 4 cm and a volume of 16 cm3. Calculate: A) the-example-1
User Kelvin Low
by
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1 Answer

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Answer:

a) Height of the pyramid is 3 cm.

b) Height of 12 cm and length of 16 cm

Explanation:

A) Finding the height of the pyramid with square base and given volume

The volume V of a pyramid is given by the formula:

V = 1/3 * (base area) * height

The base area A is a square with side length of 4 cm, so:

A = side_length^2 = 4^2 = 16 cm^2

So, we can solve the volume formula for height:

height = V / (1/3 * A) = 16 cm^3 / (1/3 * 16 cm^2)

Doing the calculation, we find:

height = 16 cm^3 / (5.333 cm^2) = 3 cm

So, the height of the pyramid is 3 cm.

B) Finding the dimensions of a similar pyramid with a given volume

The volume of a similar pyramid is proportional to the cube of the scale factor (because volume is a three-dimensional measurement). So, if we let k be the scale factor, then:

V2 = k^3 * V1

We can solve for k:

k = (V2 / V1)^(1/3)

Then we can find the height and side length of the base of the similar pyramid as:

height2 = k * height1

side_length2 = k * side_length1

In this case, V1 is 16 cm^3, V2 is 1024 cm^3, height1 is 3 cm, and side_length1 is 4 cm. So:

k = (1024 cm^3 / 16 cm^3)^(1/3) = 4

So:

height2 = 4 * 3 cm = 12 cm

side_length2 = 4 * 4 cm = 16 cm

So, the similar pyramid with a volume of 1024 cm^3 has a height of 12 cm and a base side length of 16 cm.

User Koterpillar
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