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slega [8]
3 years ago
8

Find the volume of each pyramid or come. Round to the nearest tenth if necessary.

Mathematics
1 answer:
Naya [18.7K]3 years ago
7 0

QUESTION 1

The given pyramid has a square base.

The volume of this square pyramid is given by;

V=\frac{1}{3}\times l^2\times h

where l=5ft is the length of a side of the square base.

and h=8ft is the height of the pyramid.

We substitute the values into the formula to get;

V=\frac{1}{3}\times 5^2\times 8 ft^3

V=66.7 ft^3

QUESTION 2

The given pyramid has a rectangular base.

The volume of this rectangular pyramid is given by;

V=\frac{1}{3}\times l\times b\times h

where l=7cm and w=4cm are the length and width  of a side of the rectangular base.

and h=8cm is the height of the pyramid.

We substitute the values into the formula to get;

V=\frac{1}{3}\times 7\times 4\times 8cm^3

QUESTION 3

The given pyramid has a rectangular base.

The volume of this rectangular pyramid is given by;

V=\frac{1}{3}\times l\times b\times h

where l=10in. and w=8in are the length and width  of a side of the rectangular base respectively.

There is a right triangle created inside this pyramid that can help us find the height of this pyramid.

Notice that the base of this right triangle is half the width of the rectangular base (4in.) and the hypotenuse is 14in.

We need to use Pythagoras Theorem to find the height of this pyramid.

h^2+4^2=14^2

h^2+16=196

h^2=196-16

h^2=180

h=\sqrt{180}

h=6\sqrt{5}in.

We substitute the values into the formula to get;

V=\frac{1}{3}\times 10\times 8\times6\sqrt{5}in^3

V=160\sqrt{5}in^3

V=357.8in^3

QUESTION 4

The radius of the base of the given cone is 12m.

The height of the cone is 25m.

The volume of a cone is calculated using the formula;

V=\frac{1}{3}\pi r^2h

We substitute the given values to get;

V=\frac{1}{3}\pi 12^2\times 25m^3

V=3769.9m^3

QUESTION 5

The given cone has diameter 14yd.

The radius is half the diameter, r=7yd

The radius(7yd), the height (h), and the slant height(25yd being the hypotenuse) form a right triangle.

We apply the Pythagoras Theorem again to get;

h^2+7^2=25^2

h^2+49=625

h^2=625-49

h^2=576

h=\sqrt{576}

h=24

The height of the cone is 24yd.

The volume of a cone is calculated using the formula;

V=\frac{1}{3}\pi r^2h

We substitute the given values to get;

V=\frac{1}{3}\pi 7^2\times 24yd^3

V=1231.5yd^3

QUESTION 6

The height of the given cone is 18mm.

The radius can be calculated using the tangent ratio.

\tan(66\degree)=\frac{18}{r}

r=\frac{18}{\tan(66\degree)}

r=8.0141yd

The volume of a cone is calculated using the formula;

V=\frac{1}{3}\pi r^2h

We substitute the given values to obtain;

V=\frac{1}{3}\pi 8.0141^2\times 18mm^3

V=151.1mm^3

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Komok [63]

If I am understanding this right, since the <em>c </em>is a variable, you'd have to solve the equation and have the variable in the and result.

the sqrt525^7 = 3359983566.19

So you'd have to simplify this and add the <em>c</em> to the end of it. Unless your work is fractions.

(I take Algebra II I should be more confident on this topic, this is just what makes the most sense)

7 0
3 years ago
Read 2 more answers
b) How many ways can you deal cards (from a deck of 52) to 4 people when each player gets 7 cards. 2 hidden and 5 visible. Assum
Mariana [72]

Answer:

{52 \choose 7}{45 \choose 7}{38 \choose 7}{31 \choose 7}{7 \choose 2}^4

Step-by-step explanation:

The dealing of the cards can be seen in the following way:

We first have to choose which 7 cards are going to be dealt to the 1st player. So we have to pick 7 cards out of the 52 available cards. This can be done in {52 \choose 7} ways. Now that we have chosen which 7 cards are going to be dealt to the 1st player, we have to choose which 2 of them are going to be the hidden ones. So we have to pick 2 cards out of the 7 cards to be the hidden ones. This can be done in {7 \choose 2} ways. At this point we now know which cards are being dealt to the 1st player, and which ones are hidden for him. Then we have to choose which 7 cards to deal to the 2nd player, out of the remaining ones. So we have to pick 7 out of 52-7=45. (since 7 have been already dealt to the 1st player). This can be done in {45 \choose 7}. Then again, we have to pick which 2 are going to be the hidden cards for this 2nd player. So we have to pick 2 out of the 7. This can be done in {7 \choose 2} ways. Then we continue with the 3rd player. We have to choose 7 cards out of the remaining ones, which at this point are 52-7-7=38. This can be done in {38 \choose 7}. And again, we have to choose which ones are the hidden ones, which can be chosen in {7 \choose 2} ways. Finally, for the last player, we choose 7 out of the remaining cards, which are 52-7-7-7=31. This can be done in {31 \choose 7} ways. And choosing which ones are the hidden ones for this player can be done in {7 \choose 2} ways. At the end, we should multiply all our available choices on each step, to get the total choices or total ways to deal the cards to our 4 players (since dealing the cards is a process of several steps with many choices on each step).

{52 \choose 7}{7 \choose 2}{45 \choose 7}{7 \choose 2}{38 \choose 7}{7 \choose 2}{31 \choose 7}{7 \choose 2}={52 \choose 7}{45 \choose 7}{38 \choose 7}{31 \choose 7}{7 \choose 2}^4

7 0
3 years ago
HELP! I put the formula but I don’t know the radius
ahrayia [7]

Answer:

C. 8,624

Step-by-step explanation:

recall that the formula for circumference is

Circumference = 2πr  ( = given as 85 meters)

hence,

85 = 2πr

r = 85/(2π)

given h = 15m

volume of cylinder

= πr²h

= π (85/2π)² 15  (using calculator and assuming π = 3.14)

= 8628.58

Comparing with the choices, the closest choice (within rounding error) is C. 8,624

8 0
3 years ago
A Japanese bullet train travels 558 miles per 3 hours A. What is the rate B. How far does the train travel in 1 hour WHO EVER A
Delicious77 [7]

Answer:

Step-by-step explanation:

Remark

The rate is going to be the same as the distance travelled in 1 hour. The units will be different.

Formula

d = r * t

Givens

d = 558 miles

t = 3 hours

Problem A

r = d / t

r = 558/ 3 = 186 miles / hr

Problem B

Givens

r = 186 miles / hour

t = 1 hour

d = ?

Solution

d = 186 mi/hr * 1 hr

d = 186 miles

<u>Note</u>

This looks really trivial, but it's not. You have to learn to see the difference between a number and its units. It's not very often that the numbers will be the same, but if the units differ, then it is an entirely different question.

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Answer:

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