A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose 1/10 degree every 1/4 hour for
1 answer:
Answer:
The rate is degree per hour.
Step-by-step explanation:
Given : A scientist conducted an experiment. Due to chemical reaction, the temperature of a compound rose degree every
hour for a limited time.
To find : What was the rate, in degrees per hour that the temperature of the compound rose ?
Solution :
In every hour the temperature of a compound rose
degree
To get the rate, in degrees per hour,
In every 1 hour the temperature of a compound rose is
degree
degree/hr
degree/hr
Therefore, the rate is degree per hour.
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Option A: The height of the cylinder is equal to the diameter of the sphere.
Option C: The radius of the sphere is half the height of the cylinder.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Solution:
The sphere is inside the cylinder.
Let r be the radius of the sphere.
Option A: The height of the cylinder is equal to the diameter of the sphere.
The sphere is fully occupied the cylinder.
If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.
Option B: The height of the cylinder is two times the diameter of the sphere.
That is h = 2d. From the above option, we know that h = d.
So, it is not true.
Option C: The radius of the sphere is half the height of the cylinder.
we know that diameter = 2 × radius (d = 2r)
From option A, we have h = d.
Substitute d = 2r, we get
⇒ h = 2r
Divide by 2 on both sides, we get
Therefore, it is true.
Option D: The diameter of the sphere is equal to the radius of the cylinder.
It is not true, because diameters of both cylinder and sphere are equal.
Option E: The volume of the sphere is two-thirds the volume of the cylinder.
Radius of cylinder and sphere = r
Height of cylinder h = 2r (by option C)
Volume of cylinder = Volume of sphere
(formula)
Hence it is true.
Option A, option C and option E are true.