Question

please help!!

Mary has a cone that has a radius of 5cm and height of 10cm. James has a pyramid with base length of 10cm and height of 5cm. Which solid has a larger volume?

Answer 1

The cone has a larger volume.

Explanation:

The volume of a cone is given by:

`V_(c) = (1)/(3)\pi r^(2)h_(c)`

Where:

r: is the radius = 5 cm

`h_(c)`: is the height of the cone = 10 cm

Then, the volume of a cone is:

`V_(c) = (1)/(3)\pi (5 cm)^(2)*10 cm = 261.8 cm^(3)`

Now, the volume of a pyramid is:

`V_(p) = (1)/(3)A_(b)*h_(p)`

Where:

`A_(b)`: is the area of the base

`h_(p)`: is the height of the pyramid = 5 cm

The area of the base can be calculated as follows:

`A_(b) = l^(2) = (10 cm)^(2) = 100 cm^(2)`

Hence, the volume of the pyramid is:

`V_(p) = (1)/(3)100 cm^(2)*5 cm = 166.7 cm^(3)`

Therefore, the cone has a larger volume.

I hope it helps you!