elizabethfayebe
contestada

Solid A is similar to Solid B. If the volume of Solid A is 3,240 meters cubed
and the volume of Solid B is 15 meters cubed, find the ratio of the surface
are of Solid A to Solid B. *
O 216:1
O 36:1
O 6:1
O 18:1

Respuesta :

Option B: 36 : 1 is the ratio of the surface area of Solid A to Solid B

Explanation:

Given that the Solid A is similar to Solid B.

The volume of Solid A is 3240 m³

The volume of Solid B is 15 m³

We need to find the ratio of the surface area of Solid A to Solid B.

Thus, we have,

[tex]\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\sqrt[3]{\frac{3240}{15}}[/tex]

Dividing the terms, we get,

[tex]\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\sqrt[3]{\frac{216}{1}}[/tex]

Taking cube root, we get,

[tex]\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\frac{6}{1}[/tex]

Squaring the ratios, we get,

[tex]\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=(\frac{6}{1})^2[/tex]

[tex]\frac{SA \ of \ Solid A}{SA \ of \ Solid B}=\frac{36}{1}[/tex]

Thus, the ratio of the surface area of Solid A to Solid B is 36 : 1

Hence, Option B is the correct answer.

ashishdwivedilVT

The ratio of the surface area of Solid A to Solid B is 36 : 1.

What is Surface area?

The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid.

Here,

The Solid A is similar to Solid B.

The volume of Solid A is 3240 m³

The volume of Solid B is 15 m³

We need to find the ratio of the surface area of Solid A to Solid B.

Thus, we have,

[tex]\frac{SA of solid A}{SA of solid B}[/tex] = [tex]\sqrt[3]{\frac{3240}{15} }[/tex]

Dividing the terms, we get,

[tex]\frac{SA of solid A}{SA of solid B}[/tex] = [tex]\sqrt[3]{216}[/tex]

Taking cube root, we get,

[tex]\frac{SA of solid A}{SA of solid B}[/tex] = 6

Squaring the ratios, we get,

[tex]\frac{SA of solid A}{SA of solid B}[/tex] = [tex]\frac{36}{1}[/tex]

Thus, the ratio of the surface area of Solid A to Solid B is 36 : 1.

Learn more about Surface area from:

https://brainly.com/question/2835293

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