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How could you change the height of a cone so that its volume would remain the same when its radius was tripled?
V1 = (1/3)(pi)(r12)(h1)
V2 = (1/3)(pi)(xr12)(h2)
V1 = V2 , which means that:
(1/3)(pi)(r12)(h1) = (1/3)(pi)(xr12)(h2)
Divide both sides by (1/3)(pi) and you get:
(r12)(h1) = (xr12)(h2)
-> (r12)(h1) = x2(r12)(h2)
Divide both sides by (r12) and you get:
h1 = x2(h2)
-> h2 = (h1)/x2
For example: Cone1: r1 = 10, h1 = 10
Cone2: r2 = 30, h2 = (10/32) = 10/9 = 1.11111111
Then to check: Volume of a cone = (1/3)(pi)(r2)(h)
V1 = (1/3)(pi)(102)(10)
V1 = 1047.197551 = V2
1047.197551 = (1/3)(pi)(302)(h2)
h2 = 1047.197551/((900pi)/3)
h2 = 1.111111111 = 10/9
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How would you changed the height of a cone so that its volume would remain the same when its radius was tripled?
V = (pi) R^2 H/3 if radius triples then volume goes as radius squared = 9 times more, so you would need to reduce height by 9 to keep same volume
How do you change the height of a square pyramid so that its volume would remain the same when the area of the base is tripled?
It must be made a third of its current value, ie divided by 3. The volume of a pyramid is 1/3 x area_base x height. The 1/3 is constant; to keep the volume constant as the base_area changes, the height must vary inversely. If the base_area is tripled, ie multiplied by 3, the height must be reduced to a third, ie divided by 3.
How do you calculate the coordinates of chord given the length of radius and chord?
You cannot. If you rotate the circle around its centre, the lengths of the radius and chord will remain the same but the coordinates of the chord will change.
What happens to the volume of the rectangular prism in number 1 if the length is tripled?
I'd need to review what happened in number-1 before I could answer that. I do know that if only the length of a rectanguar prism is tripled, while the other two dimensions remain unchanged, then its volume triples.
What happens to the area of a circle if yo double the radius?
Nothing - if you double the radius you will get the diameter. The area of the circle will remain the same
How would you changed the height of a cone so that its volume would remain the same when its radius was tripled?
V = (pi) R^2 H/3 if radius triples then volume goes as radius squared = 9 times more, so you would need to reduce height by 9 to keep same volume
How do you change the height of a square pyramid so that its volume would remain the same when the area of the base is tripled?
It must be made a third of its current value, ie divided by 3. The volume of a pyramid is 1/3 x area_base x height. The 1/3 is constant; to keep the volume constant as the base_area changes, the height must vary inversely. If the base_area is tripled, ie multiplied by 3, the height must be reduced to a third, ie divided by 3.
What will happen to youngs modulus of steel if radius is doubled?
young modulus remain unaffected ...as it depends on change in length ..
How do you calculate the coordinates of chord given the length of radius and chord?
You cannot. If you rotate the circle around its centre, the lengths of the radius and chord will remain the same but the coordinates of the chord will change.
What happens to the volume of the rectangular prism in number 1 if the length is tripled?
I'd need to review what happened in number-1 before I could answer that. I do know that if only the length of a rectanguar prism is tripled, while the other two dimensions remain unchanged, then its volume triples.
When a triangle is enlarged by a factor 3 are the angles tripled in size?
No - if the lengths of the sides are all increased by a factor of 3, the angles remain unchanged. You just wind up with a "similar" triangle 3 times the size of the original. A quick counterexample would be to consider what would happen if the angles DID change. The sum of the angles in the original triangle should be 180°. If the angles in the new, larger triangle tripled in size, the sum of the angles in the bigger triangle would be 540° - but the sum of the angles of a triangle should always remain 180°.
What happens to the area of a circle if yo double the radius?
Nothing - if you double the radius you will get the diameter. The area of the circle will remain the same
What happens to the surface area of a cylinder if the height is doubled and the diameter of the base is not change?
The surface area of the 'wall' doubles, but the base areas remain the same.
Would the height of a tree be greater in feet or inches?
The height would remain the same.
What happens to kinetic energy if the velocity is tripled?
If velocity is tripled, the kinetic energy of an object will increase by a factor of nine. This is because kinetic energy is directly proportional to the square of the velocity according to the equation KE = 0.5 * m * v^2.
When a rock is placed in a graduated cylinder containing water the height of the water will what?
remain the same
What does not change when a physical change in a sample occurs?
Substance in the material Remain the same
