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lozanna [386]
2 years ago
15

Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere

A to sphere B? 2:6 4:36 1:3 1:27
Mathematics
2 answers:
krok68 [10]2 years ago
7 0

Answer:

1:27 (D)

Step-by-step explanation:

Given:

Sphere A has a diameter of 2

Sphere A is dilated to create sphere B

Scale factor = 3

Volume of a sphere = 4/3 πr³

Radius = r = diameter/2 = 2/2

r = 1

Volume of sphere A = 4/3 ×π(1)³

Volume of sphere A = 4/3 × π

Volume of sphere B = 4/3 πR³

Since the diameter was dilated, the diameter of B = diameter of A × scale factor

diameter of B = 2×3 = 6

Radius of B = R = diameter/2 = 3

Volume of sphere B = 4/3 × π(3)³

Volume of sphere B = (4/3)(27)π

Ratio of the volume of sphere A to volume of sphere B

= [4/3 ×π]: [(4/3)(27)π]

= (4π/3)/[(4π/3)×27] = 1/27

= 1:27

kondor19780726 [428]2 years ago
4 0

Answer: 1:27

Step-by-step explanation:

The original volume * scale factor cubed = new volume.

The scale factor is 3 and 3^3 is 27, so the ratio is 1:27

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Step-by-step explanation:

First, we have to determine the multiplicative factor of the dimensions for both figures.

Considering sides AB and WX,

multiplicative factor = \frac{12}{8}

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So that:

XY = 6 x 1.5 = 9

YZ = 7 x 1.5 = 10.5

ZW = 7 x 1.5 = 10.5

Perimeter of ABCD = 6 + 7 + 7 + 8

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Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12

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The ratio of the perimeters of the two quadrilaterals can be determined as;

ratio = \frac{perimeter of ABCD}{Perirmeter of WXYZ}

       = \frac{28}{42}

       = \frac{2}{3}

The ratio of the perimeter of ABCD to perimeter of WXYZ is \frac{2}{3}.

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2 years ago
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artcher [175]

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

From the Venn diagram, n(AUB)=31

The given probabilities in the option are calculated below:

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