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The outer diameter of a spherical tank measures 6 feet. If the tank is made with a material 4 inches thick, estimate the volume of water it can hold.

A. 29 cu. ft
B. 876.5 cu. ft
C. 99.8 cu. ft
D. 106 cu. ft

Answer :

The estimated volume of water that the spherical tank can hold using given diameter and thickness is equal to d. 106 cubic feet.

Outer diameter of a spherical tank = 6 feet

Thickness of tank using material = 4 inches

To estimate the volume of water that a spherical tank can hold,

Consider the internal dimensions of the tank.

The outer diameter of the tank measures 6 feet.

Since the tank has a material thickness of 4 inches,

Subtract twice this thickness from the outer diameter to obtain the internal diameter.

Internal diameter = Outer diameter - 2 × Material thickness

= 6 feet - 2 × (4 inches / 12 feet per inch)

= 6 feet - 2 × (1/3) feet

= 6 feet - (2/3) feet

= 5 1/3 feet

Now that we have the internal diameter,

calculate the radius of the tank,

Radius

= Internal diameter / 2

= (5 1/3 feet) / 2

= 2 2/3 feet

To find the volume of the tank, use the formula for the volume of a sphere,

Volume = (4/3) × π × Radius³

= (4/3) × 3.14159 × (2 2/3 feet)³

≈ 106 cubic feet

Therefore, the estimated volume of water that the spherical tank can hold is approximately d. 106 cubic feet.

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Rewritten by : Jeany