Help me please 3/7

Match each spherical volume to the largest cross sectional area of that sphere

zlopas [31]

Answer:

Part 1) $324\pi\ units^{2}$ ------> $7,776\pi\ units^{3}$

Part 2) $36\pi\ units^{2}$ ------> $288\pi\ units^{3}$

Part 3) $81\pi\ units^{2}$ ------> $972\pi\ units^{3}$

Part 4) $144\pi\ units^{2}$ ------> $2,304\pi\ units^{3}$

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

$A=324\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$324\pi=\pi r^{2}$

Solve for r

$r^{2}=324$

$r=18\ units$

Find the volume of the sphere

The volume of the sphere is

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

For $r=18\ units$

substitute

$V=\frac{4}{3}\pi (18)^{3}$

$V=7,776\pi\ units^{3}$

Part 2) we have

$A=36\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$36\pi=\pi r^{2}$

Solve for r

$r^{2}=36$

$r=6\ units$

Find the volume of the sphere

The volume of the sphere is

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

For $r=6\ units$

substitute

$V=\frac{4}{3}\pi (6)^{3}$

$V=288\pi\ units^{3}$

Part 3) we have

$A=81\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$81\pi=\pi r^{2}$

Solve for r

$r^{2}=81$

$r=9\ units$

Find the volume of the sphere

The volume of the sphere is

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

For $r=9\ units$

substitute

$V=\frac{4}{3}\pi (9)^{3}$

$V=972\pi\ units^{3}$

Part 4) we have

$A=144\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$144\pi=\pi r^{2}$

Solve for r

$r^{2}=144$

$r=12\ units$

Find the volume of the sphere

The volume of the sphere is

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

For $r=12\ units$

substitute

$V=\frac{4}{3}\pi (12)^{3}$

$V=2,304\pi\ units^{3}$

5 0

3 years ago

Read 2 more answers

1) Graph both equation and identify the point of intersection. y=2x+3 x+2y=8

Verizon [17]

Answer:

Intersection Point: (0.4, 3.8)

General Formulas and Concepts:

Algebra I

Solving systems of equations by graphing

Step-by-step explanation:

Step 1: Define Systems

y = 2x + 3

x + 2y = 8

Step 2: Graph

Where the 2 lines intersect is the solution set to the systems of equations.

5 0

3 years ago

Seven hundred new chairs were delivered to a school. If each class

Natalija [7]

Answer:

24 chairs in each class needed

25 classrooms

700 chairs total

how many extra chairs

chairs will be c

t is total

t= 25×c

opposite of multiplication is division( 25 is multiplying by c) c needs to be alone

25 classrooms times chairs equal total chairs

t is 700

700=25×c

700/25=25/25c

700/25=C

c is 28

so 28 chairs for 25 classrooms

they need 24 chairs per class

so there are 4 extra chairs per class

4×25 is 100

**or just multiply 25 classes and 24 chairs

25 times 24 is 600

there are 700 chairs

100 left over

so 100 extra chairs

4 0

3 years ago

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You are working on an urban planning project assessing the growth of a city. Five years ago, the population was 134,785 The curr

Firdavs [7]

To calculate growth rate, start by subtracting the past value from the current value. Then, divide that number by the past value. Finally, multiply your answer by 100 to express it as a percentage.

Explanation:

The "population growth rate" is the rate at which the number of individuals in a population increases in a given time period, expressed as a fraction of the initial population. Population growth is based on four fundamental factors: birth rate, death rate, immigration, and emigration.

Annual Growth Rate of Population refers to the rate at which the number of individuals in a given popular increase over a year, expressed as a fraction of the initial popular of the previous years. The annual percentage growth rate of population is the percent growth divided by the number of years.

8 0

3 years ago

Why is math so hard to figure out

balu736 [363]

Answer:

ask the teacher

Step-by-step explanation:

3 0

3 years ago

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