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Complete the table with the ratios of the base areas, surface areas, and volumes of these two similar cones. Assume the ratios are written in the form cone A : cone B.

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Respuesta :

The ratio of the base areas and ratios of volume are respectively; 1/9 and 1/27

How to find the surface area of a cone?

A) Base area of cone has the formula;

A_b = 3V/h

where;

V is volume

h is vertical height

Since the ratio of both heights is 5:15 = 1:3, then;

Ratio of base areas = 1²/3² = 1/9

B) Formula for volume of a cone is;

V = ¹/₃πr²h

Thus;

V_a = ¹/₃π(r²)5

V_a = ⁵/₃π(r²)

V_b = ¹/₃π(R²)15

Thus;

V_a/V_b = ⁵/₃π(r²)/¹/₃π(R²)15

From earlier, we saw that;

r²/R² = 1/9. Thus;

V_a/V_b = (1/3) * (1/9)

V_a/V_b = 1/27

Read more about Cone surface area at; https://brainly.com/question/6613758

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