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
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
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