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3 years ago

⦁ A sphere is inscribed in a cube with a volume of 27 cm3. What is the volume of the sphere?

Mathematics

1 answer:

lyudmila [28]3 years ago

4 0

Answer:

≈ 14.14 cm³

Step-by-step explanation:

First find the side length of the cube.

V=S³

27=S³

∛27=∛s³

3=S

Then the volume of the sphere.

V= $\frac{4}{3}$ × π(pi) × r³(radius cubed)

V= $\frac{4}{3}$ × π(pi) × (1.5³)

= $\frac{9}{2}$ π cm³ ≈ 14.14 cm³

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Application of Geometric Series

Gnoma [55]

Answer:

7.2224

Step-by-step explanation:

The value of the summation is given by the formula ...

Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.

Your sum has first term and ratio ...

a1 = 2(0.6) . . . . . summation term for n=1

r = 0.6

So the sum is ...

$\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112$

Then the value of the entire given expression is ...

$\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}$

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A calculator can help you find the value.

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1 year ago

Marshall drove to work in rush hour traffic, going just 27 miles in 1 hour and 20 minutes. Later that day, he left work early to

iragen [17]

Answer:

The average speed of Marshall is 29.7 mph

Step-by-step explanation:

Given;

distance traveled to work, d₁ = 27 miles

distance traveled back home, d₂ = 27 miles

initial time taken, t₁ = 1 hour and 20 minutes

final time taken, t₂ = 29 minutes

Total distance traveled, d = d₁ + d₂ = 27 miles + 27 miles = 54 miles

Total time taken for the journey, t = t₁ + t₂ = 1 hour + ( 20 mins + 29 mins)

t = 1 hour + 49 mins = 1 hour + 0.817 hour = 1.817 hour

The average speed is given by;

v = total distance / total time

v = 54 miles / 1.817 hour

v = 29.7 mph

Therefore, the average speed of Marshall is 29.7 mph

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2 years ago

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Step-by-step explanation:

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Natali5045456 [20]

39 is 60% of 65.
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2 years ago

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