For prisms and pyramids, how are the area of the base of the solid and the shape of the solid related to the volume

For prisms of equal distribution its volume is the product of its base area and height.

Step-by-step explanation:

We find that the lateral area in a pyramid is double the height

yet 1/3 volume for 1cm^2 base.

We find that the lateral area in a pyramid is four x  the height with 2cm*2 base yet 1 1/3  volume for 2cm^2 base.

So the increase changes in shift to the square and the base 3 x and +1 for the volume from 1 unit bases to 2 unit bases that share the same height.

Disc within a sphere can sometimes reflect low unit 1/4 when they are the same radius.

Circle area  = A=πr2   for 1cm radius = 3.14

Sphere = V=4/3πr3 for 1cm radius = 4.19 (we can see the extra 1.05 represents the fraction increase. However for larger than 1 unit volume equations, we would also account for the square of such radius.

Where working out the formula for the volume of a sphere is 4/3 times pi times the radius cubed. Cubing a number means multiplying it by itself three times, in this case, the radius times the radius times the radius. To find the volume in terms of pi, leave pi in the formula rather than converting it to 3.14.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.