Question

1. As shown in the diagram below, the radius of a cone is 2.5 cm and its

Answer 1

The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³

Calculating the volume of a cone

From the question, we are to determine the volume of the cone

The volume of a cone can be calculated by using the formula,

$V = \frac{1}{3} \pi r^{2} h$

Where V is the volume

r is the radius

and h is the height

From the given information,

radius, r = 2.5 cm

slant height, l = 6.5 cm

First, we will determine the height of the cone

By Pythagoras' theorem

$l^{2} = r^{2} + h^{2}$

Where $l$ is the slant height

r is the radius

and h is the height of the cone

Then, we can write that

$6.5^{2} = 2.5^{2} + h^{2}$

$42.25 = 6.25 + h^{2}$

$h^{2}=42.25 - 6.25$

$h^{2} =36$

$h = \sqrt{36}$

∴ h = 6 cm

Now, putting the parameters into the equation for the determining the volume of a cone, we get

$V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6$

$V = \pi \times 6.25\times 2$

$V = 12.5 \pi$ cm³ OR 39.27 cm³

Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³

Learn more on Calculating volume of a cone here: brainly.com/question/12004994

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