Question

Given the length of each side of the base of a square pyramid is 2r, the radius of the cone is

r, and the heights are the same. By how much is the square pyramid bigger than the cone?

a)
2
2
2
2
​

b)
3
2
3
2
​

c)
4
2
4
2
​

d)
5
2
5
2
​

Answer 1

To compare the sizes of the square pyramid and the cone, calculate their volumes and compare them. The square pyramid is 4/pi times bigger than the cone, which is approximately 1.27 times bigger.

Step-by-step explanation:

To compare the sizes of the square pyramid and the cone, let's first calculate their respective volumes. The volume of a square pyramid is given by V = (1/3) * (side length)^2 * height, and the volume of a cone is given by V = (1/3) * pi * (radius)^2 * height. Since the heights are the same, we can compare the volumes by dividing the volume of the square pyramid by the volume of the cone.

The volume of the square pyramid is V1 = (1/3) * (2r)^2 * h = (4/3) * r^2 * h.

The volume of the cone is V2 = (1/3) * pi * r^2 * h.

Now, let's divide V1 by V2: V1/V2 = [(4/3) * r^2 * h] / [(1/3) * pi * r^2 * h].

The h's in the numerator and denominator cancel out, leaving us with V1/V2 = (4/3) * r^2 / (1/3) * pi * r^2. The r^2 in the numerator and denominator also cancel out, so we are left with V1/V2 = (4/3) / (1/3) * pi = 4/pi.

Hence, the square pyramid is 4/pi times bigger than the cone. Since pi is approximately 3.14, the square pyramid is approximately 1.27 times bigger than the cone. Therefore, the square pyramid is bigger than the cone by a factor of 1.27.