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Andru [333]
3 years ago
15

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a

nd radius r. A cylinder with height h and radius r. What is the volume of the sphere? 6 meters cubed 7 meters cubed 14 meters cubed 28 meters cubed
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0

Answer:

14 meters cubed

Step-by-step explanation:

Volume of cylinder:

pi × r² × (2r)

2pi × r³ = 21

pi × r³ = 10.5

Volume of sphere:

(4/3) × pi × r²

(4/3) × 10.5

14 m³

8090 [49]3 years ago
5 0

Answer:

C. 14 metres cubed

Step-by-step explanation:

The volume of a sphere is denoted by: V=\frac{4}{3} \pi r^3, where r is the radius, while the volume of a cylinder is denoted by: V=\pi r^2h, where r is the radius and h is the height.

Here, we know that the sphere and cylinder have the same radius and height. However, the "height" of the sphere is technically just the diameter, which is twice the radius. So, h = 2r. We know the volume of the cylinder is 21, so:

V=\pi r^2h=\pi r^2*2r=2\pi r^3

21=2\pi r^3

πr³ = 21/2 = 10.5

Now plug this into the volume of a sphere formula:

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

V=\frac{4}{3} *10.5=14

The answer is C, 14 metres cubed.

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6 0
3 years ago
The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. Th
e-lub [12.9K]

Answer:

95% of monthly food expenditures are between $110 and $190.

Step-by-step explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side, \bar{x}-2\sigma

To the right side, \bar{x}+2\sigma

We have given,

The sample mean \bar{x}=\$150

The standard deviation \sigma=\$20

Substitute in the formula,

\bar{x}-2\sigma

=150-2(20)

=150-40

=110

\bar{x}+2\sigma

=150+2(20)

=150+40

=190

Therefore, 95% of monthly food expenditures are between $110 and $190.

6 0
3 years ago
In a recent
qwelly [4]

Answer:collecting data

Step-by-step explanation:

7 0
2 years ago
Explain how do you know that 712 is greater than 1/3 but less than 2/3
Rudik [331]

Answer:

712 is bigger than 1/3 and 2/3.

Step-by-step explanation:

Because it is whole number, while 1/3 and 2/3 are fraction of whole number.

Did you mean 7/2?

5 0
3 years ago
Bicycle license plates in Flatville each contain three letters. The first is chosen from the set ({C,H,L,P,R}) the second from (
amm1812
5\cdot3\cdot4=60 - the current possible number of plates

after adding 2 letters into the 1st set:
7\cdot3\cdot4=82
after adding 2 letters into the 2nd set:
5\cdot5\cdot4=100
after adding 2 letters into the 3rd set:
5\cdot3\cdot6=90
after adding 1 letter into the 1st set and 1 into the 2nd set:
6\cdot4\cdot4=96
after adding 1 letter into the 1st set and 1 into the 3rd set:
6\cdot3\cdot5=90
after adding 1 letter into the 2nd set and 1 into the 3rd set:
5\cdot4\cdot4=80

<span>The largest possible number of plates after adding two numbers is 100.
So, </span><span>the largest possible number of additional plates is 100-60=40</span>
7 0
3 years ago
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