What is the height of a right rectangular prism with a length of 2cm a width of 10cm and a volume of 75cm^3? Write the answer in decimal form
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
Given:
Length (l) = 2 cm
Width (w) = 10 cm
Volume (V) = 75 cm^3
Using the formula V = lwh:
75 = 2 * 10 * h
75 = 20h
h = 75 / 20
h ≈ 3.75
Therefore, the height of the right rectangular prism is approximately 3.75 cm.
Eduardo has a 32 gallon fish tank. Describe what this measurement means.
Fish tank holds 32 gallons of water
Fish tank is 32 feet long
Fish tank is too big
Fish tank holds 32 fish
The measurement "32 gallon fish tank" means that the fish tank has a capacity to hold 32 gallons of water. This means that the tank can hold a volume of water equivalent to 32 gallons.
It does not mean the fish tank is 32 feet long, as the measurement is given in gallons, not feet.
It also does not necessarily mean that the fish tank is too big, as the size of a 32-gallon fish tank can be appropriate for various sizes of fish or aquatic animals.
Lastly, it does not mean that the fish tank holds 32 fish, as the capacity of a fish tank is often measured by volume (gallons) rather than the number of fish it can accommodate.
A delivery truck service needs to transport 75 boxes. The boxes are all cubes with a side of 18 in. How much space will the service need to transport the boxes? Use the formula for the volume of the cube
The formula for the volume of a cube is V = s^3, where s is the length of a side of the cube.
Given:
Number of boxes = 75
Side length of the cube (s) = 18 inches
Using the formula V = s^3:
Volume of one cube = 18^3 = 5832 cubic inches
To find the total space needed to transport 75 boxes:
Total volume = Volume of one cube * Number of boxes
Total volume = 5832 * 75 = 437,400 cubic inches
Therefore, the delivery truck service will need approximately 437,400 cubic inches of space to transport 75 boxes, each with a side length of 18 inches.
Anna Beth has a freshwater fish tank and a saltwater fish tank. They are both cubes. The side length of the fresh water is 15 cm. The side length of the saltwater fish tank is 45 cm. How many times larger is the volume of the saltwater tank than the volume of the freshwater tank?
To find the volume of each cube fish tank, we use the formula V = s^3, where s is the length of a side of the cube.
For the freshwater fish tank:
Side length (s1) = 15 cm
Volume1 = s1^3 = 15^3 = 3375 cubic cm
For the saltwater fish tank:
Side length (s2) = 45 cm
Volume2 = s2^3 = 45^3 = 91125 cubic cm
To find how many times larger the volume of the saltwater tank is than the volume of the freshwater tank:
Volume ratio = Volume2 / Volume1
Volume ratio = 91125 / 3375
Volume ratio = 27
So, the volume of the saltwater fish tank is 27 times larger than the volume of the freshwater fish tank.