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
natka813 [3]
1 year ago
15

8 A clock in the shape of an hour glass is made up of two identical cones

Mathematics
1 answer:
ra1l [238]1 year ago
4 0

Answer:

The two cones are aligned on edge to edge so that the total volume of the hourglass becomes 2∗13πr2h

Step-by-step explanation:

a) When the sand has y units left in the upper cone the height of the cone becomes y, the radius remains 1cm.Now let's take the right triangle In the upper coneAnd by similar triangles property we found that the radius of the cone in which the amount of sand is left is y3 unitsNow the volume of the sand in the remaining part of the upper cone isπy32y which gives πy327Now if we apply the same similar triangle property with the cone in the below we find that the radius of the part it has filled up remains the same as y3unitsSo the volume it has filled is (3-y) from the top cone which says that the volume filled on the bottom cone has a height of (3-y)So therefore the volume of the frustum which it has filled up isπ3h(R2+r2+rR) {Is the volume of the frustum with two radii r and R with a height h}i.eπ3(3−y)(12+(y/3)2+(y/3))So now the total volume of the hourglass in terms of y is π3(3−y)(12+(y/3)2+(y/3))+πy327b) The next question tells us that when the height of the sand in the below cone reaches up a height of h centimetreswhich is exactly 3-y in the previous questionso substituting y = h-3 in the previous question we'll find the volume of the hourglass in terms of hπ(h−3)327+π3(6−h)(12+((h−3)/3)2+((h−3)/3)) .c) Total volume of the hourglass isV=V1+V2⇒3π4=πy327+π−π27(3−h)3Putting h=1We have the value of y as⇒3π4=π27y3+π+π278..............(1)⇒y=(54)13Differentiating the first equation with respect to t we have0=π9y2dydt+π9(3−h)2dhdtPutting values that dydt=−0.14inches/sec at h =1 and for ⇒y=(54)13We have0=π9(54)132∗(−0.14)+π922dhdt⇒0.1956π9=4π9dhdt⇒dhdt=0.19564⇒dhdt=0.0489

You might be interested in
Simplify (-36x)(-1/3)(2/9)(-4y)
den301095 [7]

Answer:

\frac{32xy}{3}

Step-by-step explanation:

3 0
3 years ago
Help OvO with this math question-
harkovskaia [24]

Answer:

C

Step-by-step explanation:

40 x 80 = 3200

120 x 100 = 12000

3200 + 12000 = 15200

6 0
2 years ago
Read 2 more answers
Does (2, 3) make the inequality 2x + 5y &lt; 20 true?<br> yes<br> no
Svetlanka [38]

Answer:

Yes

Step-by-step explanation:

Hopefully this helps!

4 0
2 years ago
Read 2 more answers
8(5b + 3) = 10(4b + 2)
Kitty [74]

Answer:

=40b+24

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
4friends shared a pitcher of juice 6/24 2/16 5/16 4/32 which 2 would have drank 1/4 of the juice
Annette [7]
6/24 and 5/16 are the two friends who would have drank 1/4 of the juice.
3 0
3 years ago
Other questions:
  • a ramp 29 ft long rises to a platform. the bottom of the platform is 20 ft from the foot of the ramp. find x, the angle of eleva
    13·1 answer
  • Ryan throws a baseball upward with an initial velocity of 12 m/s from a height of 2m above the ground. How long will it take for
    11·1 answer
  • Determine whether the sequences are increasing, decreasing, or not monotonic. If increasing, enter 1 as your answer. If decreasi
    13·1 answer
  • Many inches in 2 feet i nches =2 feet
    10·2 answers
  • Give three solutions of the inequality 6 − 11x &lt; 61.
    8·2 answers
  • PLS HURRY I'M BEING TIMED I'LL GIVE BRAINLIEST
    10·1 answer
  • 2 1 11 __ ft of fabric is needed to make pants, while 4 1 6 _ ft of fabric is required to make a rug. How much more fabric is ne
    7·1 answer
  • What is the value of x in the equation x + 5.1 = 0?
    5·2 answers
  • -8(2a + 3b) + 5 (6 + -4d)
    12·1 answer
  • For a complex number written in polar form, its representation is unique as long as the argument is restricted to
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!