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melamori03 [73]
2 years ago
12

The volume of a sphere can be found using the formula V = πr . If the sphere has a diameter of 10x y z mm, what is the volume of

the sphere in cubic millimeters?
Mathematics
1 answer:
viva [34]2 years ago
8 0

Answer:

<em>500πx³y³z³ </em>

Step-by-step explanation:

Volume of a sphere = 4πr³

r is the radius of the sphere

Given

Diameter of the sphere = 10xyz mm

Radius = diameter/2

Radius = 10xyz/2

Radius = 5xyz

Substitute the radius into the formula

Volume of the sphere = 4π(5xyz)³

Volume of the sphere = = 4π(125)x³y³z³

Volume of the sphere = 500πx³y³z³

<em>Hence the volume of the sphere is 500πx³y³z³ mm³</em>

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Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first establish that triangle BCD is a right-angle triangle.

Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:

a^2 + b^2 = c^2

Where c = hypotenus of right-angle triangle

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Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:

Let a = BC

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c = DB = 26

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Therefore, as a = BC, BC = 10.

If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:

a = BC = 10

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

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676 = 676

FINAL ANSWER:

Therefore, BC is equivalent to 10.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3
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