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Math  /  Geometry

QuestionFigure A: 3-Dimensional Figu (b) 18minsx18 \mathrm{mins} x

Studdy Solution

STEP 1

What is this asking? We need to find the pool's **volume** in cubic feet, then figure out how many gallons of water are needed to fill it to **95% capacity**. Watch out! Don't forget to convert cubic feet to gallons at the end!
Also, we're dealing with 95% capacity, not 100%!

STEP 2

1. Calculate the total volume
2. Calculate the 95% volume
3. Convert to gallons

STEP 3

Alright, let's **dive in**!
We've got a rectangular prism, and finding its volume is as easy as multiplying its length, width, and height.
It's like stacking building blocks, but with water!

STEP 4

So, we **multiply**: Volume=Length⋅Width⋅Height \text{Volume} = \text{Length} \cdot \text{Width} \cdot \text{Height} .
We have Length=20 feet \text{Length} = 20 \text{ feet} , Width=13 feet \text{Width} = 13 \text{ feet} , and Height=7 feet \text{Height} = 7 \text{ feet} .

STEP 5

Plugging in the numbers, we get: Volume=20 ft⋅13 ft⋅7 ft=1820 ft3 \text{Volume} = 20 \text{ ft} \cdot 13 \text{ ft} \cdot 7 \text{ ft} = 1820 \text{ ft}^3 .
Boom! That's the **total volume** of our pool in cubic feet.

STEP 6

Now, we only want to fill it to **95% capacity**.
Think of it like leaving a little room at the top so you don't splash water everywhere when you do a cannonball!

STEP 7

To find 95% of the total volume, we **multiply** the total volume by 0.95 (because 95% is the same as 0.95).

STEP 8

So, 0.95⋅1820 ft3=1729 ft3 0.95 \cdot 1820 \text{ ft}^3 = 1729 \text{ ft}^3 .
This is the volume of water we need.

STEP 9

Almost there!
We've got our volume in cubic feet, but we need it in gallons.
There are approximately 7.48 gallons in every cubic foot.
It's a magical conversion factor!

STEP 10

To convert, we **multiply** our 95% volume in cubic feet by this conversion factor: 1729 ft3⋅7.48gallonsft3 1729 \text{ ft}^3 \cdot 7.48 \frac{\text{gallons}}{\text{ft}^3} .
Notice how the ft3\text{ft}^3 units divide to one, leaving us with gallons!

STEP 11

Crunching the numbers, we get 1729⋅7.48≈12933.92 gallons 1729 \cdot 7.48 \approx 12933.92 \text{ gallons} .
And there we have it!

STEP 12

We need approximately **12933.92 gallons** of water to fill the pool to 95% capacity.

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