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These cones are similar. Find the volume of the smaller cone. Round to the nearest tenth. 2 cm 5 cm Volume=[?]cm^ 3 Volume me = 131 cm ^ 3

These Cones Are Similar Find The Volume Of The Smaller Cone Round To The Nearest Tenth 2 Cm 5 Cm Volumecm 3 Volume Me 131 Cm 3 class=

Sagot :

Answer:

8.4 cm^3 to the nearest tenth.

Step-by-step explanation:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

So:

5^3 / 2^3 = 131 / v

v = 2^3 * 131 / 5^3

= 8 * 131 / 125

= 8.384.

The volume of smaller cone is 8.4 cm³

What is Volume of Cone?

The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone. According to the geometric and mathematical concepts, a cone can be termed as a pyramid with a circular cross-section. By measuring the height and radius of a cone, you can easily find out the volume of a cone. If the radius of the base of the cone is "r" and the height of the cone is "h", the volume of cone is given as V = (1/3)πr²h.

By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.

We know, h² + r² = L²

⇒ h = √(L² - r²)

where,

h is the height of the cone,

r is the radius of the base, and,

L is the slant height of the cone.

The volume of the cone in terms of slant height can be given as V = (1/3)πr²h = (1/3)πr²√(L² - r²).

Given:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

Then,

5³ / 2³ = 131 / v

v = 2³ * 131 / 5³

v = 8 * 131 / 125

v = 8.384 cm³

Learn more about volume here:

https://brainly.com/question/1984638

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