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1 year ago

Match each three-dimensional figure to its volume based on the given dimensions. (Assume π = 3.14.)

Mathematics

2 answers:

pochemuha1 year ago

8 0

a right cylinder with radius 4 cm

and height 3 cm = 150.72 cu cm

a pyramid with base area

16 sq cm and height 30 cm = 160 cu cm

a pyramid with a square base of

length 3 cm and height 16 cm = 48 cu cm

a cone with radius 5 cm and

height 12 cm = 314 cu cm

LekaFEV [45]1 year ago

3 0

Answer:

The volume of the cylinder is 150.72 cm³ ⇒ last answer

The volume of the cone is 314 cm³ ⇒ 1st answer

The volume of the pyramid is 160 cm³ ⇒ 2nd answer

The volume of the pyramid is 48 cm³ ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the volumes of some shapes

- The volume of the cylinder of radius r and height h is:

V = π r² h

- The volume of the cone of radius r and height h is:

V = 1/3 π r² h

- The volume of the pyramid is:

V = 1/3 × its base area × its height

* Lets solve the problem

# A cylinder with radius 4 cm and height 3 cm

∵ V = π r² h

∵ π = 3.14

∵ r = 4 cm , h = 3 cm

∴ v = 3.14 (4)² (3) = 150.72 cm³

* The volume of the cylinder is 150.72 cm³

# A cone with radius 5 cm and height 12 cm

∵ V = 1/3 π r² h

∵ π = 3.14

∵ r = 5 cm , h = 12 cm

∴ V = 1/3 (3.14) (5)² (12) = 314 cm³

* The volume of the cone is 314 cm³

# A pyramid with base area 16 cm² and height 30 cm

∵ V = 1/3 × its base area × its height

∵ The area of the base is 16 cm²

∵ The height = 30 cm

∴ V = 1/3 (16) (30) = 160 cm³

* The volume of the pyramid is 160 cm³

# A pyramid with square base of length 3 cm and height 16 cm

∵ V = 1/3 × its base area × its height

∵ The area of the square = s²

∵ The area of the base = 3² = 9 cm²

∵ The height = 16 cm

∴ V = 1/3 (9) (16) = 48 cm³

* The volume of the pyramid is 48 cm³

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Step-by-step explanation:

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The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

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X 0 1 2 3

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We can calculate the expected value with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

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$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

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The variance is calculated with this formula:

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Step-by-step explanation:

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$Green = 20$

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Required

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From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

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This is then solved further as:

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2 years ago

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So the right options are:

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Further explanation:

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The co-efficient of x is the slope of the line

So,

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Let m1 be the slope of required line

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Putting the value of slope

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Putting (-5,1) in the equation to find the value of b

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Putting the values of slope and b in equation

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Multiplying the whole equation by 5 will give us:

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Another form of equation of line is Point-slope form

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Putting the values of slope and point in the equation, we get

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So the right options are:

$y=-\frac{2}{5}x-1$

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Keywords: Point-Slope form, Parallel lines

Learn more about point slope form at:

#LearnwithBrainly

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