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3 years ago

11

Consider this composite figure made of a cone and a cylinder. A cone has a height of 8 centimeters and radius of 3 centimeters.

A cylinder has a height of 7 centimeters and radius of 3 centimeters. What is the volume of the cone?

1 answer:

dangina [55]3 years ago

3 0

The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.

Step-by-step explanation:

The given is,

Composite figure made of a cone and a cylinder.

A cone has a height of 8 centimeters and radius of 3 centimeters.

A cylinder has a height of 7 centimeters and radius of 3 centimeters.

Step:1

Volume of composite figure = Volume of Cone +

Volume of cylinder............(1)

Step:2

Formula for volume of cone,

$Volume of cone, V_{cone} = \pi r^{2} \frac{h}{3}$ ....................(2)

Where, r - Radius of cone

h - Height of cone

From the given,

r = 3 centimeters

h = 8 centimeters

Equation (2) becomes,

$= \pi (3^{2} )(\frac{8}{3})$

$=\pi (9)(2.667)$

= (3.14 × 9 × 2.667) (∵ $\pi$ = 3.1415)

= 75.4

$Volume of cone, V_{cone}$ = 75.4 cubic centimeters

Step:3

Formula for volume of cylinder,

$Volume of cone, V_{cone} = \pi r^{2} h$ ....................(2)

Where, r - Radius of cylinder

h - Height of cylinder

From the given,

r = 3 centimeters

h = 7 centimeters

Equation (2) becomes,

$= \pi (3^{2} )(7)$

$=\pi (9)(7)$

= (3.14 × 9 × 7) (∵ $\pi$ = 3.1415)

= 197.92

$Volume of cylinder, V_{cylinder}$ = 197.92 cubic centimeters

Step:4

Equation (1) becomes,

Volume of composite figure = 75.4 + 197.92

= 273.32 cubic centimeters

Result:

The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.

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Stolb23 [73]

Answer:

log (16)=2 in base 3x-5

==>16=2^(3x-5)

==>2^4=2^(3x-5)

==>4=3x-5

==>3x=9

==>x=3

Step-by-step explanation:

4 0

3 years ago

A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.

Pachacha [2.7K]

a) Probability of both being males is 27%

b) Probability of both being females is 23%

c) Probability of having exactly one male and one female is 50%

Step-by-step explanation:

a)

The probability that the birth is a male can be written as

$p(m) = 0.52$ (which corresponds to 52%)

While the probability that the birth is a female can be written as

$p(f) = 0.48$ (which corresponds to 48%)

Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:

$p(mm)=p(m)\cdot p(m)$

And substituting, we find

$p(mm)=0.52\cdot 0.52 = 0.27$

So, 27%.

b)

In this case, we want to find the probability that both children are female, so the probability

$p(ff)$

As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:

$p(ff)=p(f)\cdot p(f)$

And substituting

$p(f)=0.48$

We find:

$p(ff)=0.48\cdot 0.48=0.23$

Which means 23%.

c)

In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:

- The probability that 1st child is a male and 2nd child is a female, namely $p(mf)$

- The probability that 1st child is a female and 2nd child is a male, namely $p(fm)$

So, this probability is

$p(mf Ufm)=p(mf)+p(fm)$

We have:

$p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25$

$p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25$

Therefore, this probability is

$p(mfUfm)=0.25+0.25=0.50$

So, 50%.

Learn more about probabilities:

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5 0

3 years ago

10 points, please help

pochemuha

Answer: 8 inches

Explanation:
a^2 + b^2 = c^2
6^2 + b^2 = 10^2
36 + b^2 = 100
b^2 = 64
(Have to find the square root of 64)
= 8 inches

7 0

2 years ago

Read 2 more answers

Sam bought a new skateboard. The sales tax rate is 6%. The equation to find the total cost is where c is the cost of the skatebo

sp2606 [1]

The independent variable is the cost of the skateboard, c.

The dependent variable would be the total cost, t.

The best way to understand this is that the cost of the skateboard from the company is not going to change based on a sales tax rate., But the overall total cost could change depending on what the sales tax rates are.

The total cost would be dependent upon the sales tax rate.

7 0

3 years ago

What’s the answer?!!!!

mel-nik [20]

Answer: YES

Step-by-step explanation:

<u>Concept</u>

In a right triangle, the square of both legs is equal to the length of hypotenuse squared. This is the Pythagorean theorem: a²+b²=c². For more graphical explanation, please refer to the attachment below.

<u>Given</u>

Leg a = 36 in

Leg b = 48 in

Hypotenuse c = 60 in

<u>Solve</u>

a² + b² = c²

(36)² + (48)² = 3600

(60)² = 3600

3600 = 3600

Therefore, the answer is <u>YES</u>

Hope this helps!! :)

Please let me know if you have any questions

6 0

3 years ago