Mathematics, 10.01.2020 23:31 deku6

a sphere with a mass of 12 g has a radius measuring 2 cm. what is its density?

0.36 g/cm3
1.43 g/cm3
6 g/cm3
24 g/cm3

Answers: 3

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The density of the sphere with mass 12 g and radius 2 cm is 0.36 g/cm³. The correct option is the first one (0.36 g/cm3)

From the question,

The mass of the sphere is 12 g and

The radius is 2 cm.

To determine its density,

From the formula

$Density =\frac{mass}{volume}$

Therefore, we will first determine the volume of the sphere.

Volume of a sphere is given by the formula

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

Where is the volume of the sphere

and is the radius of the sphere

Take $\pi = 3.14159$

From the question, $r = 2 \ cm$

Put these values into the equation,

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

$V = \frac{4}{3}\times 3.14159 \times 2^{3}$

$V = \frac{4}{3}\times 3.14159 \times 8$

$V = \frac{100.53088}{3}$

$V = 33.51029 \ cm^{3}$

Now, for the density

Put the values of the volume and mass in the equation

$Density =\frac{mass}{volume}$

From the question, mass = 12 g

From above, V = 33.51029 cm³

∴ $Density =\frac{12 \ g}{33.51029 \ cm^{3} }$

$Density = 0.3581 \ g/cm^{3}$

Density ≅ 0.36 g/cm³

Hence, the density of the sphere with mass 12 g and radius 2 cm is 0.36 g/cm³. The correct option is the first one (0.36 g/cm3)

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Answer from: csciahetano

Density=mass/volume

The volume of a sphere is:

V=(4πr^3)/3 so

d=3m/(4πr^3), we are given that r=2cm and m=12g

d=36/(32π) g/cm^3

d=1.125/π g/cm^3

d≈0.358 g/cm^3

d≈0.36 g/cm^3 (to nearest hundredth of a gram per cm^3)

Answer from: Quest

answer for #1 is c

answer for #2 is d

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Answer from: Quest

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:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

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

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

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a sphere with a mass of 12 g has a radius measuring 2 cm. what is its density?

0.36 g/c...

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