The volume of an object is equal to the ratio of its mass to density, v = . the mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter. what is the radius of the grape? round to the nearest tenth of a centimeter.

Step-by-step explanation:

Mass = Volume x density

Mass = 8.4 gm

Density = 2.4 g/cc

Substituting

       8.4 = Volume x 2.4

       Volume = 3.5 cm³

We need to find radius, r

Substituting volume value

Radius of grape = 1 cm  

To solve the problem we must know about volume.

The radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

The volume can be defined as the space occupied by the three-dimensional object.

It is given by the ratio of mass(m) and density(ρ).

Given to us

Mass of the object, m = 8.4 grams

Density of the object, ρ = 2 gram/cm³

As it is already mentioned that the volume is equal to the ratio of its mass to density. therefore,

Thus, the volume of the object is 4.2 cm³.

To find the radius of the sphere we will use the formula of the volume of the sphere.

Substitute the values,

Hence, the radius of the sphere is whose mass is 8.2 grams and has a density of 2 grams per cubic centimeter is 1 cm.

Learn more about Volume:

link

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!