If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2, what is the height of this prism?
Let the length of the prism be x, the width be y, and the height be z. We are given:
- Volume = 1.5 in^3
- Length * width = 1.5 in^2
Using the formula for the volume of a rectangular prism, we can write:
V = lwh
Substituting the given values, we get:
1.5 = xy*z
Also, we know that:
xy = 1.5
Multiplying both sides of the equation by x, we get:
x*xy = 1.5x
x^2*y = 1.5x
Substituting this into the formula for volume, we get:
1.5 = x^2*y*z
Substituting xy = 1.5, we get:
1.5 = 1.5xz
Simplifying, we get:
z = 1 in
Therefore, the height of the prism is 1 inch.
Lloyd bought a refrigerator that measures 76 cm×76 cm×170 cm to fit in a space with a volume of 975,000 cm3. Will the refrigerator fit in the space? Explain.
To determine if the refrigerator will fit in the space, we need to compare its volume to the volume of the space. The volume of the refrigerator is given by:
76 cm x 76 cm x 170 cm = 1,095,680 cm^3
The volume of the space is given as 975,000 cm^3.
Since the volume of the refrigerator is greater than the volume of the space, it will not fit in the space. The refrigerator is too large for the given space, as its volume exceeds the space’s capacity.
Therefore, Lloyd needs to find a larger space or a smaller refrigerator to fit it in the given space.
A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?
The volume of a rectangular pyramid can be calculated using the formula:
V = (1/3) * base area * height
In this case, the base of the pyramid is a rectangle with width 4 cm and length 9 cm, so its area is:
A = width * length = 4 cm * 9 cm = 36 cm^2
The height of the pyramid is 21 cm. Therefore, the volume of the slice of cheese is:
V = (1/3) * 36 cm^2 * 21 cm = 252 cm^3
Therefore, the volume of the piece of cheese is 252 cubic centimeters.
To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism: V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Given that the volume is 1.5 in^3, we can plug it into the equation: 1.5 = lw * h.
Next, we are given that the length and width have a product of 1.5 in^2. So, we can write an equation for this relationship: lw = 1.5.
Now, we can substitute this value into the equation for volume: 1.5 = 1.5 * h.
To find the value of h, we can divide both sides of the equation by 1.5: h = 1.5 / 1.5.
Hence, the height of the prism is 1 inch.