Mathematics, 31.10.2019 19:31, cookiee1387

The ratio of the volumes of the similar solids is 25: 1 5: 1 125: 1
the ratio of the surface areas of the similar solids is 125: 1 5: 1 25: 1
the ratio of the heights of the similar 125: 1 5: 1 25: 1
two spheres with different radii measurements similar (always, never sometimes)
the length of the diameter of a sphere is 8 inches. the volume of the sphere the surface area of the sphere. (less than, greater than, equal to)

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answered: marieknight689

Part 1)

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c) The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2) Two spheres with different radii measurements are always similar

Part 3) The volume of the sphere is greater than the surface area of the sphere

Step-by-step explanation:

Part 1) we know that

The ratio of the corresponding heights of the similar solids is equal to the scale factor

The ratio of the surface areas of the similar solids is equal to the scale factor squared

The ratio of the volumes of the similar solids is equal to the scale factor elevated to the cube

In this problem

The scale factor is 5/1

therefore

a) The ratio of the heights of the similar solids is 5/1

b) The ratio of the surface areas of the similar solids is (5/1)²=25/1

c) The ratio of the volumes of the similar solids is (5/1)³=125/1

Part 2)

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.

In this problem to prove that two spheres are similar, a translation and a scale factor (from a dilation) will be found to map one sphere onto another.

therefore

Two spheres with different radii measurements are always similar

Part 3) The length of the diameter of a sphere is 8 inches

The volume of the sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=8/2=4\ in$ -----> the radius is half the diameter

substitute

$V=\frac{4}{3}\pi (4)^{3}$

$V=85.33\pi\ in^{3}$

The surface area of the sphere is equal to

$SA=4\pi r^{2}$

substitute

$SA=4\pi (4)^{2}$

$SA=64\pi\ in^{2}$

therefore

The volume of the sphere is greater than the surface area of the sphere

answered: Guest

Letter c i’d say
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chemists are often responsible for designing a chemical reaction and analyzing the products obtained from it. one significant part of designing a chemical reaction is determining the amount of each reactant that is needed and the amount of each product that will be produced. in order to do so, chemists use stoichiometry, the quantitative relationships between reactants and products.