23.3k views
3 votes
Given the rectangular prism

1) determine the height

2) calculate the area of the bottom base/face

3) the rectangular prism has a volume of 1200 cm (cubed). How many kilometers of water can the prism hold?

Given the rectangular prism 1) determine the height 2) calculate the area of the bottom-example-1

2 Answers

3 votes

1) 15 cm

- To determine the height, let’s do the Pythagorean Theorem,
a^(2) + b^(2) = c^(2).
- Let’s input it now!
8^(2) + b^(2) = 17^(2)
- Plug it into a calculator.
64 + b^(2) = 289
- Change the format.
289 - 64 = b^(2)
- Simplify.
225 = b^(2)
- Take the square root.
√(225) = 15

2) 80 squared cm

- Let’s use the formula, bh (base × height)
- 10 × 8 = 80


3) 1.2 × 10 to the power of -12 km³

- There are 1 billion cm³ in a km³, so 1200/1 billion would be 1.2 × 10 to the power of -12


—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

User Jeffrey Sweeney
by
7.5k points
6 votes

Answer:

1) height = 15cm

2) Base Area = 80cm²

3)
\sf 1.2 * 10^(-12) cubic kilometers

Explanation:

Let's address each part of the question:

1) Determine the height:

For the rectangle face, we can use the Pythagorean theorem since we know the diagonal (
\sf 17\, \textsf{cm}) and one side (
\sf 8\, \textsf{cm}). Let
\sf h be the height.


\sf h = \sqrt{\textsf{diagonal}^2 - \textsf{length}^2}


\sf h = √(17^2 - 8^2) \, \textsf{cm}


\sf h = √(289 - 64) \, \textsf{cm}


\sf h = √(225) \, \textsf{cm}


\sf h = 15 \, \textsf{cm}

So, the height of the rectangular prism is
\sf 15\, \textsf{cm}.


\hrulefill

2) Calculate the area of the bottom base/face:

For the bottom base, the area (
\sf A_{\textsf{base}}) is given by the product of the length and width.


\sf A_{\textsf{base}} = \textsf{length} * \textsf{width}


\sf A_{\textsf{base}} = 10 * 8 \, \textsf{cm}^2


\sf A_{\textsf{base}} = 80 \, \textsf{cm}^2

So, the area of buttom base/face = 80 cm².


\hrulefill

3) Calculate the volume of the rectangular prism and convert to kilometers cubed:

Given that the volume (
\sf V) is
\sf 1200\, \textsf{cm}^3, to convert this volume to kilometers cubed, we divide by
\sf 1,000,000,000,000 (since there are
\sf 1,000,000,000,000 cubic centimeters in a cubic kilometer).


\sf V_{\textsf{kilometers}^3} = (1200)/(1,000,000,000,000) \, \textsf{kilometers}^3


\sf V_{\textsf{kilometers}^3} = 1.2 * 10^(-12) \, \textsf{kilometers}^3

So, the rectangular prism can hold
\sf 1.2 * 10^(-12) cubic kilometers of water.

User Gev
by
8.0k points