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How are the volumes of cones and pyramids related to the volumes of prisms and cylinders?
A cone is 1/3 of the volume of a cylinder with the same base and height. A pyramid is 1/3 of the volume of a prism with the same base and height.
Are two scalene triangles always similar?
yes. they are always the same but a different scale.
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.
Is two regular polygons always sometimes or never similar?
If they have the same nuber of sides (angles) then always. If not then never. So, overall, I suppose the answer is sometimes - depending on the number of sides.
Is it true to say that two equiangular triangle are always equal?
No. Equiangular only implies the angles are the same, but says nothing about the lengths. Two equiangular triangles are always similar, only sometimes congruent.
Can two right cones with the same height and base radius have different lateral areas?
No, they cannot.
Is your shadow always the same height?
NO.
How are the volumes of cones and pyramids related to the volumes of prisms and cylinders?
A cone is 1/3 of the volume of a cylinder with the same base and height. A pyramid is 1/3 of the volume of a prism with the same base and height.
What is the height of a sphere with a diameter of 3.8?
A sphere's height will always be the same as its diameter.
Does a cone with a circle base and a cone with a square base have the same volumes?
no The area of a cone is 1/3 times the base times the height, so the volumes are the same only if the area of the base times the height is the same in both cones.
How can you recognize similar figures?
They have the same measure of base and height.
Is there pollen cones and seed cones on the same trees?
Yes, in case of Pinus pollen producing cones (male cones) and seed producing cones (female cones) are present on the same plant. Such plants are called monoecious.
Does similar polygons always have the same area?
no. similar polygons do not have the same area. similar just means that they have the same angle measurements and are proportional.
Will girls always be the same height as their mothers?
No only sometimes
Are the two tides that occur a day always the same height?
No
Explain why similar figures are not always congruent?
similar figures have the same angles but not necessarily the same side lengths
What type of triangle is always similar to all other triangles of the same type?
90 degree triangles are always similar.
