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How are the area of the base and the volume of that solid related?
Which solid?? For the same height, larger area of base = larger volume. So they are directly related.
How do you convert the volume of a prism into the volume of a pyramid that has the same base area and height?
formula of the volume of a prism = (base area)(height) formula of the volume of a pyramid = (1/3)(base area)(height) therefore, to convert the volume of a prism to that of a pyramid, just divide it by 3
Two rectangular prisms that have the same volume and the same height would their base be different or the same?
They would have to have the same base area, if that's what you mean.
Are trapezoids and isosceles trapezoids the same?
Yes
How are volume and surface area the same when volume stays the same?
There is no reason for the surface area to remain the same even if the volume is the same.
Name two trapezoids that have the same height and area but have different base lengths?
Nope
How are the area of the base and the volume of that solid related?
Which solid?? For the same height, larger area of base = larger volume. So they are directly related.
How do you convert the volume of a prism into the volume of a pyramid that has the same base area and height?
formula of the volume of a prism = (base area)(height) formula of the volume of a pyramid = (1/3)(base area)(height) therefore, to convert the volume of a prism to that of a pyramid, just divide it by 3
Two rectangular prisms that have the same volume and the same height would their base be different or the same?
They would have to have the same base area, if that's what you mean.
Are trapezoids and isosceles trapezoids the same?
Yes
The volume of a cone compared to the volume of a cylinder?
If the area of the base and the height of the cylinder and the cone are the same, then the volume of the cone will always be one third of the volume of the cylinder.
How do you find the volume of a pentagonal pyramid?
Basically, the same as the volume of any other pyramid: the volume is (1/3) x base x height. The "base" refers to the area of the base; for instance, if the base is a regular pentagon, use the formula for a regular pentagon.
Why does the volume quadruple when the radius of a cylinder is doubled?
The volume is Base x height; the Base area is the same as the formula for a circle - which is proportional to the square of the radius. For example, if you double the radius (or the diameter, or the circumference) of a circle, its area will quadruple.
How are the area of the base and volume similar?
They are not except trivially. They are both geometric concepts, they both have an even number of letters of which every odd one is a consonant and the even ones are vowels, they both end in the letter "e". The area of the base is a two-dimensional measure whereas volume is a three dimensional concept. Two objects with the same base area can have totally different volumes - even if they have the same height. Consider, for example a cone and a cylinder with the same circular base. Conversely, two shapes with the same volume can have totally different base area. Just consider a brick that is turned around so that a different face becomes its base.
How are volume and surface area the same when volume stays the same?
There is no reason for the surface area to remain the same even if the volume is the same.
The volume of wax in the candle shown is 2262 cm 3 which equation can be used to find h the height of the candel in centimeters?
Assuming that the cross section of the candle is the same everywhere (as you go down, or up), the volume is equal to the base area times the height. If you have a way to find out the base area, you can divide the volume by this base area to find the height.
What is the relationship between the height and base area?
There is no relationship, in the sense that you can have any base are with any height. For a prism shape (if the horizontal cross section is always the same as the base), the base area times the height is equal to the volume.
