Claire's old aquarium has a volume of 27,000cm3. She bought a new aquarium in which the length and width are 5 times those of her old tank. What is the volume of Claire's new aquarium?
The length and width are both 5 times those of her old tank. Because V = l*w*h, the new volume must be 5l*5w*h. Multiply the old volume by 5*5 = 25.
L=26 w=31 h= 15
To find the volume of Claire's new aquarium, we need to first determine the dimensions of the new tank. Since the length and width of the new tank are 5 times those of the old tank, we can calculate:
New length = 5 * old length
New width = 5 * old width
Next, we can find the area of the base of the new tank by multiplying the new length and new width:
Area of base = New length * New width
Finally, we multiply the area of the base by the height of the tank to get the volume:
Volume = Area of base * Height
Now let's calculate the volume of Claire's new aquarium step by step.
Given:
Volume of old aquarium = 27,000 cm^3
Step 1:
Since the old tank's volume is not given, we don't need to use it. We can directly calculate the dimensions of the new tank.
New length = 5 * old length
New width = 5 * old width
Step 2:
Let's assume the old tank had a square base, so the old length and width were the same. Consequently, the new length and width will also be the same.
New length = 5 * (old length) = 5 * (old width) = New width
Step 3:
Let's solve for the new length and width:
New length = 5 * (old length) = 5 * (sqrt(old area))
Step 4:
Now, let's calculate the area of the base of the new tank:
Area of base = New length * New width = (5 * (sqrt(old area))) * (5 * (sqrt(old area)))
Step 5:
Finally, let's find the volume of the new tank:
Volume = Area of base * Height
Volume = (Area of base) * (Height)
Volume = (Area of base) * h
Volume = (25 * old area) * Height
Therefore, the volume of Claire's new aquarium is 25 times the volume of her old aquarium, since we multiplied the old area by 25. As the old volume was 27,000 cm^3, the new volume will be:
Volume = 25 * (27,000 cm^3)
Volume = 675,000 cm^3
So, the volume of Claire's new aquarium is 675,000 cm^3.