Question

PRESLEY

Answer 1

The volume of the fountain cup in gallons is 4775.2 gallons

Volume of a frustum

Since the fountain cup is in the shape of a frustum, its volume is given by

V = πh/3(r² + rr' + r'²) where

• h = height of cup = 8 feet,
• r = radius of base of cup = 4 feet and
• r' = radius of top of cup = 6 feet.

So, substituting the values of the variables into th equation, we have

V = πh/3(r² + rr' + r'²)

V = π × 8 ft/3[(4 ft)² + 4 ft × 6 ft + (6 ft)²]

V = π × 8 ft/3[16 ft² + 24 ft² + 36 ft²]

V = π × 8 ft/3 × (76 ft²)

V = 608π ft³/3

V = 1910.088 ft³/3

V = 636.69 ft³

V ≅ 636.7 ft³

Volume of the fountain cup in gallons

Since there are 7.5 gallons per cubic foot,

The volume of the fountain cup in gallons is V = 636.7 ft³ × 7.5 gallons/ft³ = 4775.2 gallons

So, the volume of the fountain cup in gallons is 4775.2 gallons

Learn more about volume of a frustum here:

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