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4 years ago

A sphere has a diameter of 4(x+3) centimeters and a surface area of 784π square centimeters. Find the value of x.

Mathematics

1 answer:

omeli [17]4 years ago

4 0

Answer:

The value of x is $4\ cm$

Step-by-step explanation:

step 1

Find the radius of the sphere

The surface area of the sphere is equal to

$SA=4\pi r^{2}$

we have

$SA=784\pi\ cm^{2}$

substitute and solve for r

$784\pi=4\pi r^{2}$

Simplify

$r^{2}=196$

square root both sides

$r=14\ cm$

step 2

Find the diameter

Remember that

The diameter is two times the radius

$D=2(14)=28\ cm$

step 3

Find the value of x

we have

$D=28\ cm$

$D=4(x+3)\ cm$

equate the equations

$4(x+3)=28$

$(x+3)=7$

$x=7-3=4\ cm$

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3 years ago

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Nataly_w [17]

Answer:

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Step-by-step explanation:

The complete question is: Which of the following options have the same value as 30% of 81?

Group of choices is:

(A) $\frac{30}{100}\times 81 \times 100$

(B) $0.3 \times 81$

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Now, the expression given to us is 30% of 81.

Simplifying the above expression we get;

30% of 81 = $\frac{30}{100} \times 81$

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Now, we will solve each of the given options and then see which option matches with our calculation.

Option (A) is given;

$\frac{30}{100}\times 81 \times 100$ = $30 \times 81$

This doesn't match with our answer, so this option is not correct.

Option (B) is given;

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This matches with our answer, so this option is correct.

Option (C) is given;

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This doesn't match with our answer, so this option is not correct.

Option (D) is given;

$\frac{3}{10}\times 81 \times 10$ = $3 \times 81$

This doesn't match with our answer, so this option is not correct.

Option (E) is given;

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Answer:

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Given,

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