Question

A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and the lateral area of the cylinder.
(how do i explain this? also, correct answer will be marked brailnliest)

Answer 1

The word inscribed means that the sphere is inside the cylinder and its diameter is equal to the height and diameter of the cylinder. The surface area of the sphere is equal to 
                            SA (sphere) = πd²
where d is the diameter.
That of the cylinder is,
                            SA (cylinder) = πd(h + d/2)
Since h is also equal to d
                            SA (cylinder) = πd(d + d/2) = 3πd²/2
Therefore, the surface area of the cylinder is approximately 1.5 times that of the sphere. 

Answer 2

Since the sphere is inscribed in a cylinder, that means that the cylinder's height and diameter are equal. This is because, in a sphere, if you draw two lines with a point on the center and a point anywhere on the outside of a sphere, the two lines will always be equal. So because the cylinder's bases and sides are touching the sphere's "sides", "top", and "bottom", the cylinder must have the same height and diameter as the sphere. In other words, cylinder's height = cylinder's diameter = sphere's diameter. So, for example, a sphere is inscribed in a cylinder. The sphere's diameter is 4. This means that the cylinder's diameter and height must be 4. To find the lateral area of the cylinder, you would need to use L.A. = 2 * pi * r * h ----> L.A. = 16 pi. To find the surface area of the sphere, you would need to use S.A. = 4 * pi * r^2 ----> S.A. = 16 pi.

In conclusion, if a sphere is inscribed in a cylinder, then the surface area of the sphere and the lateral area of the cylinder are equal.