a.
To prove: The height
Given information:
Volume of the spherical tank is equal to Volume of the cylindrical tank.
Formula used:
Volume of the sphere:
Volume of the cylinder:
Proof:
Given the:
Volume of the sphere is equal to Volume of the cylinder
Know that the;
Volume of the sphere:
Volume of the cylinder:
So,
Factor out
Factor out
Here, prove that the height
b.
To calculate: The surface area of each tank in terms of
The surface area of spherical tank in terms of
The surface area of cylindrical tank in terms of
Given information:
Volume of the spherical tank is equal to Volume of the cylindrical tank.
Formula used:
The surface area of a sphere:
The surface area of a cylinder:
Calculation:
The expression to find the surface area of a sphere, the tower on the left;
The surface area of a sphere:
The surface area of a cylinder, the tower on the right;
The surface area of a cylinder:
The volumes of each water tower are equal:
Divide both sides by
So,
Conclusion:
The surface area of each tank in terms of
c.
To calculate: The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank. Explain what the ratio tells you about which water tower would take less material to build.
The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank is
Given information:
Volume of the spherical tank is equal to Volume of the cylindrical tank.
Concept used:
The surface area of a sphere:
The surface area of a cylinder:
Calculation:
The surface area of spherical tank =
The surface area of cylindrical tank =
Now,
The ratio of the surface area of the spherical tank to the surface area of the cylindrical tank:
Cancel
Conclusion:
The obtained ratio by calculation is
Chapter 5 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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