6. If the length of the radius of a cylinder is tripled, which statement is true?
a. The lateral surface area of the cylinder is six times greater than the original.
b. The volume of the cylinder is six times greater than the original.
c. The lateral surface area of the cylinder is three times greater than the original.***
d. The volume of the cylinder is three times greater than the original.
correct
Thanks Steve!!!
To determine the correct statement, let's analyze how changing the radius of a cylinder affects its lateral surface area and volume.
The lateral surface area of a cylinder is given by the formula A = 2πrh, where "r" is the radius and "h" is the height. If the radius is tripled, the new radius becomes 3r. Plugging this value into the formula, the new lateral surface area becomes A = 2π(3r)h = 6πrh. This means that the new lateral surface area is six times the original, so option a is incorrect.
The volume of a cylinder is given by the formula V = πr²h, where "r" is the radius and "h" is the height. If the radius is tripled, the new radius becomes 3r. Plugging this value into the formula, the new volume becomes V = π(3r)²h = 9πr²h. This means that the new volume is nine times the original, so option b is incorrect.
Hence, the correct statement is that the lateral surface area of the cylinder is three times greater than the original, as multiplying the original lateral surface area by 3 accounts for the tripling of the radius. Therefore, the answer is option c.