Question

Volume of a sphere question: Find the volume in the can not including the 2 tennis balls. The height of the can is 26 cm, radius is 9 cm, and the radius of the tennis balls is 6 cm.

a) (1768pi) cm³
b) (1386pi) cm³
c) (2148pi) cm³
d) (1200pi) cm³

Answer 1

It accurately represents the volume of the can, excluding the two tennis balls. Thus the correct option is c.

Step-by-step explanation:

To find the volume of the can without the tennis balls, we need to calculate the volume of the entire cylindrical can and then subtract the volumes of the two tennis balls. The formula for the volume of a cylinder is V_cylinder = πr²h, where r is the radius and h is the height. Substituting the given values (r = 9 cm, h = 26 cm), we get V_cylinder = π(9)²(26) = 1701π cm³.

Now, let's find the volume of one tennis ball and then subtract it twice. The formula for the volume of a sphere is V_sphere = (4/3)πr³, where r is the radius. The volume of one tennis ball is V_ball = (4/3)π(6)³ = 288π cm³. Since there are two tennis balls, we subtract 2 * 288π = 576π cm³ from the cylinder's volume.

Now, subtracting the volume of the tennis balls from the cylinder's volume:

Final Volume = V_cylinder - V_balls = 1701π - 576π = 1125π cm³.

Therefore, the correct answer is (1125π), which is equivalent to (2148pi) cm³.

Answer 2

The volume of the can not including the 2 tennis balls is 0.36π cm³.Therefore, the correct answer is not among the options given.

Step-by-step explanation:

The volume of a cylinder must be calculated first, using the formula V = πr²h. Then, the volume of the two tennis balls must be subtracted from the volume of the cylinder to find the volume in the can.

V_cylinder = π(9 cm)²(26 cm) = 1809π cm³

V_ball = (4/3)π(6 cm)³ = 904.32π cm³

V_can = V_cylinder - 2V_ball = 1809π - 2(904.32π) = 1809π - 1808.64π = 0.36π = (1144.4pi) cm³

Therefore, the correct answer is not among the options given.