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serious [3.7K]
3 years ago
8

The ratio of the lengths of the radil of two spheres is 5 : 8 what is the ratio of the surface area of the smaller sphere to the

surface area of the larger sphere
Mathematics
1 answer:
ipn [44]3 years ago
7 0

Answer:

The ratio of the small sphere’s area to that of the big one is 25:64

Step-by-step explanation:

The area of a sphere can be calculated using the formula:

A = 4 π r^2

Now, since their radii are if the ratio 5:8, we can say that the radius of the small sphere is 5 while that of the big sphere is 8

For the small sphere, the value of the area will be 4 * π * 5^2 = 100 π unit

For the big sphere, the value of the area will be 4 * π * 8^2 = 256 π unit

The ratio of the smaller sphere to the larger sphere is;

100 π : 256 π

Divide through by 4

25: 64

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Answer:

The simplyfied version would be 19/4

Show of work:

(1/4)^-2 = 4^2

3 × 8^2/3 × 1 = 12

(9/16)^1/2 = 3/4

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Convert elements to fractions:

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---------- ----

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Since the denominators are equal combine the fractions:

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---------------

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= -45/4

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4^2 = 16

16 - 45/4

16 × 4 - 45. 16 × 4 - 45

--------- ----- ----------------

4 4. 4

-> 16 × 4 - 45 = 19

= 19/4

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