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PRESLEY
You are curious about the amount of coffee that the giant fountain cup could actually hold.
The dimensions of the fountain cup are as follows:
• Height is 8 feet.
• Diameter of the top is 6 feet.
• Diameter of the base is 4 feet.
Use this formula with height, h, radius of the base, roase, and radius of the top, rtop, to determine the volume
of the cup:
(πh).
V= -((rbase)+ (rbase) (stop) + (top)).
3
There are 7.5 gallons of liquid per cubic foot.
Enter the volume, in gallons, of the fountain cup.

PRESLEY You Are Curious About The Amount Of Coffee That The Giant Fountain Cup Could Actually Hold The Dimensions Of The Fountain Cup Are As Follows Height Is 8 class=

Sagot :

oladayoademosu

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:

https://brainly.com/question/14268491

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