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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.
Answer:
Option B.
Step-by-step explanation:
Integer: A non fractional complete number is known as integer. It can be either positive or negative or zero.
For examples : ...,-3,-2,-1,0,1,2,3,...
It is a clear that the difference between two consecutive integers is 1. It means we have to add 1 in the integer to get the next integer.
We need to express "next integer after the integer n" mathematically. So, we need to add 1 in n.
Required expression
Hence, the next integer after the integer n is n+1.
Therefore, the correct option is B.
Answer:
Simplified: 40
Step-by-step explanation:
To simplify this, we need to first separate the terms in this expression. There is a property of exponents that says: We can do this same thing to simplify this expression. Next, we can simplify each of these terms.
simply becomes 4. In the other term, the
simply cancel each other and leave the 10. This means that we're left with 4*10, which is 40