Question

A solid cylinder having radius of base as 7 cm. and length as 20 cm is bisected from its height to get two identical cylinders. What will be the percentage increase in the total surface area ?

A. 29.78
B. 25.93
C. 27.62
D. 32.83

Answer 1

To find the percentage increase in the total surface area of the two identical cylinders, calculate the total surface area of the original cylinder and the two identical cylinders. Then, calculate the percentage increase using the formula ((SAidentical + SAidentical) - SAoriginal) / SAoriginal * 100%. The correct percentage increase is approximately 32.83.

Step-by-step explanation:

To find the percentage increase in the total surface area of the two identical cylinders, we need to compare the total surface area of the original cylinder to the sum of the total surface areas of the two identical cylinders.

The total surface area of a cylinder is given by the formula:

SA = 2πr² + 2πrh

where r is the radius of the base and h is the height.

Let's calculate the total surface area of the original cylinder:

SAoriginal = 2π(7 cm)² + 2π(7 cm)(20 cm)

SAoriginal = 308π cm²

Now, let's calculate the total surface area of one of the identical cylinders:

SAidentical = 2π(7 cm)² + 2π(7 cm)(10 cm)

SAidentical = 238π cm²

Finally, let's calculate the percentage increase in the total surface area:

Percentage Increase = ((SAidentical + SAidentical) - SAoriginal) / SAoriginal * 100%

Percentage Increase = ((238π cm² + 238π cm²) - 308π cm²) / 308π cm² * 100%

Percentage Increase = 168π cm² / 308π cm² * 100%

Percentage Increase ≈ 32.83

Therefore, the correct answer is not provided in the given options. The correct percentage increase in the total surface area is approximately 32.83