Calculate the mass of 5000 spherical lead shots each of diameter 3mm, given that 1 cm cubed of lead weighs 11.4g.

Answers

Answer 1

Answer:

1. The first step to answering this question is to find the volume of a single spherical lead shot and then multiply this by 5000 to find the total volume of 5000 lead shots.

So, given that the lead shots are spherical, we must use the formula for the volume of a sphere:

V = (4/3)πr^3

Given that the diameter is 3mm, we can find the radius by dividing this by 2:

r = 3/2 = 1.5 mm

From here, there are two ways to proceed; we can either covert the radius into cm, or we can continue with the mm value and then convert the resulting volume in cubic mm into cubic cm (since we are given that 1 cm cubed of lead weighs 11.4g, we can already tell that we will have to finish with a volume in cubic cm). I will show both these methods as a) and b), respectively.

a) If there are 10 mm in 1 cm, and we have a radius of 1.5 mm, then to convert this into cm we need to simply divide by 10:

1.5 mm = 1.5/10 = 0.15 cm

Now that we have our radius in cm form, we can substitute this into the formula for the volume of a sphere that we specified at the very beginning:

V = (4/3)πr^3

V = (4/3)π(0.15)^3

V = (9/2000)π cm cubed, or

0.0045π cm cubed (in decimal form)

Now that we have the volume of one lead shot, all we need to do is multiply this by 5000 to find the volume of 5000 lead shots:

0.0045π*5000 = 22.5π cm cubed

Since we already have the total volume in cm cubed, there is no need to do any more conversions.

b) In this method, we will use radius = 1.5 mm and substitute this into the general formula for the volume of a sphere again:

V = (4/3)πr^3

V = (4/3)π(1.5)^3

V = (9/2)π mm cubed, or

4.5π mm cubed (in decimal form)

Thus, to calculate the volume of 5000 lead shots, we must multiply this value by 5000:

4.5π*5000 = 22500π mm cubed

Now comes the part where we must convert this into cubic cm; to do this we simply take the value in cubic mm and divide it by 10^3 (ie. 1000). Thus:

22500π/1000 = 22.5π cm cubed

As you can see, we end up with the same answer as in a). The key here is to remember that you need to convert, so maybe write a note to yourself at the start of the question and pay close attention to the different units in both the question and your working.

2. Now that we know that the volume of 5000 spherical lead shots is 22.5π cm cubed, we need to calculate their mass.

We are given that 1 cm cubed of lead weighs 11.4 g, thus to calculate the mass of 22.5π cm cubed of lead, we need to multiply this value by 11.4. Thus:

Mass = 22.5π*11.4

= 256.5π g

Note that this is the answer in exact form. I wasn't entirely sure about the rounding required or the value of π that you were specified to use (eg. exact, 22/7, 3.14), so if you wanted me to edit the answer to reflect that or had any questions, feel free to comment below.

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There are 25 dozen cookies in the bakery. What is the total number of cookies at the bakery? Use an array area model to show your work.

Answers

Answer:

300 cookies

Step-by-step explanation:

One dozen of cookies is equivalent to 12cookies since one dozen is 12.

If one dozen is 12, then 25 dozens of cookies will be the product of 25 and the value of one dozen of cookies to have;

25 dozens of cookies = (25 × 12)cookies

= 300cookies

The total number of cookies in the bakery is 300cookies

The total number of cookies at the bakery is 300.

An array model is shown below.

To calculate the total number of cookies at the bakery, we can use an array area model.

First, let's understand what the problem is telling us. It states that there are 25 dozen cookies in the bakery. Since a dozen is equal to 12, we can say that there are 25 x 12 = 300 cookies in total.

To represent this using an array area model, we can create an array with 25 rows and 12 columns, where each cell represents one cookie. In total, we will have 25 x 12 = 300 cells in the array.

An array model can be described as:

| | | | | | | | | | | | |

Each cell represents one cookie, and the array has a total of 300 cells. Therefore, the total number of cookies at the bakery is 300.

To learn more about multiplication;

brainly.com/question/19634536

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Solve for ×. site all steroids and check your work.

3×+5=35

Answers

x=10 first u do 35-5 then u do 30/3 to get 10

3x=30<=>x=30/3<=>x=10

The probability of a spinner stopping on 3 is 1/8 The probability of the spinner stopping on 6 is 1/8 What is the probability of the spinner stopping on 3 or 6A. 1/16
B. 1/8
C. 1/64
D. 2/8
PLEASE HELP

Answers

Your answer is B 1/8 .

What symbol do you use for square root on pc?

Answers

For this case we must find the values of "a" and "b" that make the expressions equivalent:

We have:

$\sqrt {\frac {126xy ^ 5} {32x ^ 3}} =$

We take common factor "2" from the numerator and denominator:

$\sqrt {\frac {2 * (63xy ^ 5)} {2 * (16x ^ 3)}} =$

Eliminating common factors of numerator and denominator:

$\sqrt {\frac {63y ^ 5} {16x ^ 2}} =$

So, we have that the values of a and b are:

$a = 16\nb = 2$

Answer:

$a = 16\nb = 2$

Note: To write square root on pc we use sqrt

Answer:

Step-by-step explanation:

Type in "sqrt .... " or click on the "omega" icon below for a list of built-in math characters, including "√"

Plese help with geometry question 24 was a guess ! Thank you

Answers

ECD=90 ECD=x+5+3x-7=4x-2, 4x-2=90, 4x=92, 4x/4=92/4, x=23
a) 23
ECH=x+5, 23+5=28, ECH=28
b)28
HCD=3x-7, 3(23)-7, 69-7=62 HCD=62
c)62
GCF & ECH are vertical angles, GCF=28
d) 28
ECF=180, 180-28(GCF)=152, ECF=152
e) 152
DCF=90, 90+28(GCF)=118
f) 118

26. Answer 44

6x + 11 = 10x - 9

subtract 11 and 10 from both sides to get
-4x = -20 then divide that by negative 4 whicg will get you x=5 then plug in
6(5)+11=44

27. Answer 18

9x-4=158 since bisect means cut into 2 equal pieces so abd and dbc equal 79, add 4 to get 162 then divide by 9 to get x=18

29. Answer 28

2h+6+h=90

(____)
this part represents G
complementary angles are two angles that add up to 90, so subtract 6 from 90 and add the variables to get 3h=84 then divide by 3

H = 28 to check you can plug 28 into the equation

The product of 3 and a number is 12 more than the sum of the number and 26. What is the number?

Answers

The product of three and a number (3n) is 12 more than (=12 +) the sum of the number and 26 (n + 26). Put all of those together.

2n = 12 + n + 26 Combine like terms. (12 + 26)
2n = 28 + n Subtract to get the variables together. (2n - n)
n = 28

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Calculate the mass of 5000 spherical lead shots each of diameter 3mm, given that 1 cm cubed of lead weighs 11.4g.​

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Calculate the mass of 5000 spherical lead shots each of diameter 3mm, given that 1 cm cubed of lead weighs 11.4g.