1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
trasher [3.6K]
3 years ago
5

A bucket is 20cm in diameter at the open end, 12cm in diameter at the bottom, and 16cm deep. To what depth would the bucket full

a cylindrical tin 28cm in diameter. ​

Mathematics
1 answer:
Alexus [3.1K]3 years ago
8 0

The bucket has a base diameter of  12  and top opening diameter of  20 . This makes the base radius  6  and top radius  10 .

 

The bucket as shown has the bottom base of radius:

B C = 6

and the top opening of radius:

D E = 10

The depth is:

D B = 16

If we extend the lateral surface of the bucket down it will generate a cone that contains the bucket in it.

To calculate the volume of the bucket, we need to calculate the volume of the large cone with the depth of  D A , then calculate the volume of the small cone with the depth of  B A , and subtract the volume of the small cone from the volume of the large cone.

Let's let  B A = x .The two triangles  Δ A B C  and  Δ A D E are similar due to the Angle Angle theorem because they both share angle  ∠ A D E = 90 ∘  and angle  ∠ D A E .

Therefore, the ratio of their corresponding sides are equal.

B A /D A = B C /D E

x /16 + x = 6 /10

x /16 + x = 3/5

48 + 3 x = 5 x

2 x = 48

x = 24  cm

The volume of a cone is: V = 1 /3 h π r 2

The height  ( h ) , which we are calling the depth, of the small cone is  x = 24 c m  and the depth of the large cone is  x + 16 = 24 + 16 = 40 c m

V Large Cone = 1/ 3 ( 40 ) ( π ) ( 10 ) 2 = 4000 π/3 c m 3  

V Small Cone = 1 /3 ( 24 ) ( π ) ( 6 ) 2 = 288 π c m 3

V Bucket = 4000 π /3 − 288 π = 3136 π /3 c m 3

Volume of a cylinder is:

V Cylinder = π r 2 h  where  h  is the height(depth) and  r  is the radius of the base of the cylinder.

If the base of the cylinder has a diameter of  28 c m  then the radius of the base is  14 c m

( π ) ( 14 ) 2 ( h ) = 3136 π /3

196 π h = 3136 π/ 3

196 h= 3136 /3

h = 3136 /3 /196 = 3136 /588 = 5.33 c m

Let's look at the figure below:

You might be interested in
Which of the following points are more than 5 units from the point P(−2, −2)? Select all that apply. A A (2, 1) B B (4, −1) C C
netineya [11]

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:<span>

<span> |PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}</span></span>


Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.


|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5

|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6

|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4

|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \  \sqrt{25}=5

|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4


Answer: B and D





3 0
3 years ago
How to find slope intercept form for perpendicular lines
Helga [31]
To find the slope intercept form of a line perpendicular to a given equation, the first thing you need to do is to find the slope of the perpendicular line. Because lines perpendicular to one another are always have a slope that is the negative reciprocal of them, the slope of the line perpendicular to y=x would be -1 (since the slope of y=x is 1). Then, since the perpendicular line passes through the point (5, -3), you would plug in the values of the x and y into the equation
y=-1x+b to get -3=-1(5)+b.

When you simplify, solve for b to get b=2. Now that you have your slope (m=-1) and your y-intercept (b=2), you can conclude that your perpendicular equation would be y=-x+2.
3 0
3 years ago
3/6x + 9 = 8 what does x equal
Anastaziya [24]
3/6x+9=8
3x+9=8
3x=-1
x= -1/3
3 0
3 years ago
What is C’ T’ if there was a rotation ?
Simora [160]

Answer: The Answer Is 4) Hope it Helps!

Step-by-step explanation:

4 0
4 years ago
What is 50 + 9 - 6 equals
Marrrta [24]

Answer:

53

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • You owe $2,348.62 on a credit card with an 8.75% APR. You pay $300.00 toward the card at the beginning of the month. What is the
    9·1 answer
  • I am faceing north west. if i turn 180 clockwise i will be facing what
    8·2 answers
  • (-4,2) (2-3) midpoint
    12·1 answer
  • Rewrite 3x + 4y = 10 using function notation.
    9·2 answers
  • Combine like terms. 3y-4-6-3x-7y+6x+1
    8·1 answer
  • PLEASE HELP ME FAST IM SO DUMB I NEED IT SO FAST PLEASEEEE
    7·1 answer
  • Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x =
    8·1 answer
  • Wastewater is filling barrels at the rate of 11 quarts per hour. The recycling facility picks up 120 full barrels on each trip,
    7·1 answer
  • Help me <br>#no spams.. ​
    14·2 answers
  • The length of line segment AD is 6.8 cm. The length of line segment AB is 3 cm. The length of line segment BC is 1.6 cm. Find th
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!