A sphere is inscribed in a cylinder. The surface area of the sphere and the lateral area of the cylinder are equal.
true?
let r = radius of cylinder
when you draw a sphere that fits exactly inside a cylinder, you will observe that
radius of cylinder = radius of sphere, and
height of cylinder = diameter of sphere
recall that
surface area of sphere = 4*pi*r^2
and
lateral surface area of cylinder = 2*pi*r*h
since h = diameter of sphere = 2r
2*pi*r*(2r)
4*pi*r^2
thus, it's TRUE.
hope this helps~ :)
To determine whether the statement is true or false, we need to understand the surface area of both a sphere and a cylinder.
The surface area of a sphere is given by the formula A_s = 4πr^2, where r is the radius of the sphere.
The lateral area of a cylinder is given by the formula A_c = 2πrh, where r is the radius of the base and h is the height of the cylinder.
Now, let's assume that the sphere is inscribed in the cylinder, which means the sphere is perfectly contained within the cylinder. In this case, the radius of the sphere will be equal to the radius of the cylinder.
The statement says that the surface area of the sphere and the lateral area of the cylinder are equal. So, we can set up an equation to compare the two:
4πr^2 = 2πrh
Simplifying this equation, we can divide both sides by 2πr:
2r = h
This equation indicates that the height of the cylinder (h) is twice the radius of the cylinder (r).
To conclude, the statement is true if the height of the cylinder is twice the radius of the cylinder. Otherwise, it is false.