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slega [8]
3 years ago
6

A sphere is dilated by a scale factor of 1.5 to create a new sphere. How does the volume of the new sphere compare with the volu

me of the original sphere?
Mathematics
1 answer:
SashulF [63]3 years ago
6 0

Answer:

The volume of new sphere is 3.375 times greater than the volume of old sphere

Step-by-step explanation:

Let r be the radius of old sphere. This old  sphere is dilated by a scale factor of 1.5 to create a new sphere, so the radius of new sphere is R=1.5r.

The volume of the sphere can be calculated using formula

V=\dfrac{4}{3}\pi r^3

Hence,

V_{old}=\dfrac{4}{3}\pi r^3\\ \\V_{new}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi (1.5r)^3\\ \\\dfrac{V_{new}}{V_{old}}=\dfrac{\dfrac{4}{3}\pi (1.5r)^3}{\dfrac{4}{3}\pi r^3}=1.5^3=3.375

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3 years ago
The sum of ruqiyo’s age and Mohammed’s age is 117. Five times ruqiyo’s age is 9 more than 3 times mohammed’s age. How old is eac
Bess [88]

Answer:

  • 45 and 72

Step-by-step explanation:

Let the ages be r and m

<u>We have:</u>

  • r + m = 117
  • 5r = 9 + 3m

<u>Substitute m in the second equation and solve for r:</u>

  • m = 117 - r
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<u>Then m is</u>

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3 0
3 years ago
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2. 5 + (3/2i + 6i)

3. 5 + 15i/2.
5 0
3 years ago
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Traffic signs are regulated by the Manual on Uniform Traffic Control Devices​ (MUTCD). The perimeter of a rectangular traffic si
sasho [114]

The length and width of rectangular traffic sign are 40 and 30 inches respectively

<h3><u>Solution:</u></h3>

Given that,

Perimeter of rectangular traffic sign = 140 inches

Let length and width be denoted as ‘L’ and ‘B’ respectively

Given that length is 10 inches longer than its width

L = 10 + B

<em><u>The perimeter of rectangle is given as:</u></em>

Perimeter = 2( L + B)

On substituting the values, we get

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140 = 2(10 + 2B)

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Therefore, the length is L = 10 + 30 = 40

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3 years ago
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