Examples with solutions for Volume of a Orthohedron: Worded problems

Exercise #1

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

(14+30X)(14+30X)(14+30X)212121151515

Step-by-Step Solution

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

21×(14+30x)×15= 21\times(14+30x)\times15=

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

(21×14+21×30x)×15= (21\times14+21\times30x)\times15=

We solve the multiplication exercise in parentheses:

(294+630x)×15= (294+630x)\times15=

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

294×15+630x×15= 294\times15+630x\times15=

We solve each of the exercises in parentheses to find the volume:

4,410+9,450x 4,410+9,450x

Answer

4410+9450x 4410+9450x

Exercise #2

If we increase the side of a cube by 6, how many times will the volume of the cube increase?

Video Solution

Answer

63 6^3

Exercise #3

After cleaning the public quadrilateral pool,
To be completed again
we fill it with buckets,
The volume of each bucket is 8 liters.
The quadrilateral pool with a depth of 3 meters and a width of 10 meters,
How many buckets are needed to refill the pool?

Video Solution

Answer

37500

Exercise #4

A cargo ship anchored in port, its volume is 360 cm³.
The vessel is composed of 6 small vessels.
They disassembled 3 small tanks whose total volume is half of the cargo tanks.
Suggest sizes for the edges of each small tank if its height is known to be 3 meters.

Video Solution

Answer

2X10, 4X5