A plane intersects a sphere with a volume of about 44.6 cubic meters through the center of the sphere. What is the area of the cross section to the nearest tenth?
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Answered by
2
Answer:
= 15.19 m2
Step-by-step explanation:
The cross section of a sphere produced as a result of the intersection of plane by sphere would be equal to the radius of the sphere . Hence the area of the plane would be;
Volume of sphere = 44.6 m3
Volume of sphere = 4/3πr3
4/3πr3 = 44.6
Solving for radius we get,
r = 2.2 m
Now finding the area of plane;
= πr2
=π×2.2^2
=121π
= 15.19 m2
Answered by
1
The area of the cross section to the nearest tenth is 15.19 m²
Step-by-step explanation:
From question, the volume of sphere = 44.6 m³ = V
Volume of sphere is given by the formula:
V = 4/3πr³
4/3πr³ = 44.6
∴ r = 2.2 m
The cross sectional area of plane is given by the formula:
A = πr²
A = π × (2.2)²
A = 121 × π 22/7
∴ A = 15.19 m²
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