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2 years ago

A sphere has a radius of 11 feet. A second sphere has a radius of 8 feet. what is the difference of the volume of the spheres

Mathematics

1 answer:

Rufina [12.5K]2 years ago

5 0

Answer:

1092π ft³

Step-by-step explanation:

The formula for the volume of a sphere is

V = ⁴/₃πr³

1. Volume of larger sphere

V₁ = ⁴/₃π (11)³ = ⁴/₃π × 1331 = 1774⅔π ft³

2. Volume of smaller sphere

V₂ = ⁴/₃π (8)³ = ⁴/₃π × 512 = 682⅔π ft³

3. Difference of volumes

V₁ - V₂ = 1774⅔π ft³ - 682⅔π ft³ = 1092π ft³ ≈ 3431 ft³

The difference of volumes of the spheres is 1092π ft³.

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Read 2 more answers

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Answer:Gary made 15 baskets.

Susan made 10 baskets.

Bill made 17 baskets.

Step-by-step explanation:

Let x represent the number of baskets that Gary made.

Let y represent the number of baskets that Susan made.

Let z represent the number of baskets that Bill made.

Gary made 5 baskets than Susan this season. This means that

x = y + 5

Bill made 3 less than twice as many baskets as Susan. This means that

z = 2y - 3

Together, all three made 42 baskets. This means that

x + y + z = 42 - - - - - - - - - - 1

Substituting x = y + 5 and z = 2y - 3 into equation 1, it becomes

y + 5 + y + 2y - 3 = 42

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4y = 42 - 2 = 40

y = 40/4 = 10

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x = 15

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2 years ago

The length (in centimeters) of a typical Pacific halibut t years old is approximately f(t) = 200(1 − 0.956e−0.18t). Suppose a Pa

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Answer:

7.2 years

Step-by-step explanation:

$f(t) =200(1 - 0.956e^{-0.18t})$

where f(t) is the length and t is the number of years old

given the Mike measures 148 cm, we need to find out the age

So we plug in 148 for f(t) and solve for t

$148 =200(1 - 0.956e^{-0.18t})$

divide both sides by 200

$\frac{148}{200} = 1 - 0.956e^{-0.18t}$

Now subtract 1 from both sides

$-0.26= - 0.956e^{-0.18t}$

Divide both sides by -0.956

$\frac{0.26}{0.956} =e^{-0.18t}$

Now take ln on both sides

$\frac{0.26}{0.956} =e^{-0.18t}$

$ln(\frac{0.26}{0.956} )=-0.18tln(e)$

$ln(\frac{0.26}{0.956} )=-0.18t$

divide both sides by -0.18

t=7.2

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