the cube root of the volume of a cube gives the length of one side of the cube.
volume=343cm cubed
a. find the side length of the cube shown
b. find the area of each face of the cube
i have no idea how to do this!
It would help if we could draw diagrams on these boards but we can't. The problem essentially tells you how to work it.
The problem states that "the cube root of the volume of a cube gives the length of one side of the cube."
a, find the side length of the cube and it tells yoy that the volume is V = 343 cm^3. So take the cube root. Do you know how to do that on your calculator. Punch in 343, hit the y^x key and type in .3333333. My calculator returns 7.0 and you can check that by 7x7x7 = 343. So the length of the side of the cube is 7.0 cm.
b. If the sides iare 7.0 cm, then the area of a face is length x width = 7 x 7 ?? square cm
Question: The volume of a cube is 343 mm2. What is the length of one side of the cube?
@bot answer this question and explain it
What is the volume of a cube with a side length of 1.5 in.?
The formula for the volume of a cube is V = s^3, where s is the length of one side of the cube. If the side length is 1.5 in., we can plug that value into the formula:
V = (1.5 in.)^3
V = 3.375 in.^3
Therefore, the volume of the cube is 3.375 cubic inches.
answer this question and explain it
A rectangular prism has a volume of 27 in.3 If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
Since the base and height of the rectangular pyramid are congruent to the rectangular prism, the base of the pyramid must also have an area of 27 square inches.
The formula for the volume of a pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, since the base area is 27 square inches and the height is congruent to the dimension of the rectangular prism, we can substitute these values into the formula:
V = (1/3)(27 in.²)(h)
Simplifying:
V = 9h
So, to find the volume of the pyramid, we need to find the height of the pyramid. Since the height of the pyramid is congruent to one dimension of the rectangular prism, we can use the formula for the volume of a rectangular prism to find the height:
27 in.³ = lwh
Since we know that the volume of the rectangular prism is 27 in.³ and the remaining two dimensions are congruent, we have:
27 in.³ = l(w²)
w³ = 27 in.³
w = 3 in.
So, the height of the pyramid must also be 3 inches. Plugging in the values for B and h into the formula for pyramid volume, we get:
V = (1/3)(27 in.²)(3 in.)
V = 27 in.³
Therefore, the volume of the rectangular pyramid is 27 cubic inches.
make it shorter
Given that a rectangular prism has a volume of 27 in³, and if a rectangular pyramid with the same base and height as the prism is considered, we need to find the volume of that pyramid.
Since the base and height of the pyramid are congruent to the prism, the base area is 27 in². Using the formula for the volume of a pyramid, we can get the volume of the pyramid as 1/3 times the base area times the height.
The height of the pyramid is the same as one dimension of the prism. By using the formula for the volume of the prism, we can calculate the missing dimension to be 3 inches. Therefore, the height of the pyramid is also 3 inches.
Replacing the values in the volume formula of the pyramid, we get the answer as 27 cubic inches. So, the volume of the rectangular pyramid is 27 in³.
If the rectangular prism has a volume of 27 in³, then we know that:
length x width x height = 27
Since it is a rectangular prism, we can assume that the base of the rectangular pyramid is also a rectangle with the same dimensions as the base of the prism.
The height of the pyramid is not given, but we know that it is congruent to the height of the prism. Therefore, the height of the pyramid is also equal to the height of the prism.
The volume of a pyramid is given by the formula:
1/3 x base area x height
Since the base of the pyramid is a rectangle with the same dimensions as the base of the prism, the base area of the pyramid is the same as the base area of the prism. Therefore, we can substitute the base area of the prism into the formula for the pyramid:
1/3 x base area x height = 1/3 x (length x width) x height
Since the height of the pyramid is equal to the height of the prism, we can substitute the height of the prism into the formula:
1/3 x base area x height = 1/3 x (length x width) x height = 1/3 x 27
Simplifying the expression, we get:
1/3 x 27 = 9
Therefore, the volume of the rectangular pyramid is 9 in³.
make this into a much shorter explanation
Given that a rectangular prism has a volume of 27 in³, the volume of a rectangular pyramid with the same base and height can be found by using the formula 1/3 x base area x height. Since the base area is 27 in², substituting the height of the prism gives a volume of 9 in³ for the pyramid.
Make this explanation much shorter
After considering all the given data we come to the conclusion that the volume of the prism is 1440 in³, under the condition that A rectangular pyramid has a volume of 480 in. The volume of a rectangular pyramid is represented by the formula (1/3) × base area × height. Now, the volume of a rectangular prism is given by the formula base area × height. Now if we consider the rectangular prism has a base and height congruent to the pyramid, then the base area of the prism is equivalent to the base area of the pyramid. Then, the volume of the prism is equivalent to three times that of the pyramid.Hence, the volume of the pyramid is 480 in³, we can evaluate the volume of the prism Volume of prism = 3 × Volume of pyramid = 3 × (1/3) × Base area × Height = Base area × Height Then, the volume of the rectangular prism is 480 × 3 = 1440 in³. To learn more about volume