Find the volume for 3 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 3 cylinders where the height of the cylinder is the same as the diameter of the sphere.
(who ever does it I will give brainliest and answer 3 of there questions)

Answer:

Hii!!

Volume Of Sphere =[tex] \frac{4}{3} * π * r^3. [/tex]

Let r be 1cm, 3 cm, 6 cm.

So,

Volume of sphere 1 = [tex] \frac{4}{3} * 3.14 * 1^3. [/tex]

Volume of sphere 1 = 4.19 cm^3

Volume of sphere 2 = [tex] \frac{4}{3} * 3.14 * 3^3. [/tex]

Volume of sphere 2 = 113.04cm^3

Volume of sphere 3 = [tex] \frac{4}{3} * 3.14 * 6^3. [/tex]

Volume of sphere 3 = 904.32 cm^3

Volume of cylinders = [tex] π * r^2 * h. [/tex]

Let r be 1cm, 3 cm, 6 cm and h be 2cm, 6cm and 12cm respectively.

So,

Volume of cylinder 1 = [tex] π * 1^2 * 2. [/tex]

Volume of cylinder 1 = 6.28 cm^3

Volume of cylinder 1 = [tex] π * 3^2 * 6. [/tex]

Volume of cylinder 1 = 169.56 cm^3

Volume of cylinder 1 = [tex] π * 6^2 * 12. [/tex]

Volume of cylinder 1 = 1356.48 cm^3

HOPE IT HELPS!!!

BRAINLIEST PLS!!!!

We can write the volume of spheres with three different  radii as given below

[tex]\rm Let\; R_1 , R_2, R_3 \; be \; the \; three\; radii\; of \; sphere \; respectively \\\\\rm Volume \; of \; first \; sphere = (4/3) \pi \ R_1^3 \\\\\rm Volume \; of \; second \; sphere = (4/3) \pi \ R_2^3 \\\\Volume \; of \; third \; sphere = (4/3) \pi \ R_3^3[/tex]

Also we can write the the volume of the cylinders as follows

[tex]\rm Volume \; of \; first \; cylinder = \pi R_1 ^2H_1 = \pi R_1^2 (2R_1) = 2 \pi R_1^3[/tex]

[tex]\rm Volume \; of \; second\; cylinder = \pi R_2^2H_2 = \pi R_2^2 (2R_2) = 2 \pi R_2^3[/tex]

[tex]\rm Volume \; of \; third \; cylinder = \pi R_3 ^2H_3 = \pi R_3^2 (2R_3) = 2 \pi R_3^3[/tex]

Volume of a sphere with radius R is given by equation

[tex]\rm Volume \; of \; the \; sphere \; of\; radius\; R = \bold{4/3 \pi R^3 }[/tex]

[tex]\rm Let\; R_1 , R_2, R_3 \; be \; the \; three\; radii\; of \; sphere \; respectively \\\\\rm Volume \; of \; first \; sphere = (4/3) \pi \ R_1^3 ........(1) \\\\\rm Volume \; of \; second \; sphere = (4/3) \pi \ R_2^3 .........(2) \\\\Volume \; of \; third \; sphere = (4/3) \pi \ R_3^3..........(3)[/tex]

Equation (1) (2) and (3) represent the volumes of three different spheres

Given that the heights of the cylinders are equal to the diameter of the spheres

so from this given condition we can write the following relations

[tex]\rm Height\; of \; first \; sphere = H_1 = 2R_1 \\\\ Height\; of \; second \; sphere = H_2 = 2R_2 \\\\Height\; of \; third \; sphere = H_3 = 2R_3 \\\\[/tex]

The volume of the cylinder is given by equation  (4)

[tex]\rm Volume \; of \; the\; cylinder = \pi R^2 H........(4) \\\\Where R = Radius \; of \; the \; cylinder \\\\H \; is \; the \; Height \; of \; the\; cylinder\\[/tex]

From  the given conditions of heights of  cylinders  and radius of the sphere.

We can write the the volume of the cylinders as follows

[tex]\rm Volume \; of \; first \; cylinder = \pi R_1 ^2H_1 = \pi R_1^2 (2R_1) = 2 \pi R_1^3[/tex]

[tex]\rm Volume \; of \; second\; cylinder = \pi R_2^2H_2 = \pi R_2^2 (2R_2) = 2 \pi R_2^3[/tex]

[tex]\rm Volume \; of \; third \; cylinder = \pi R_3 ^2H_3 = \pi R_3^2 (2R_3) = 2 \pi R_3^3[/tex]

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