A wooden cylinder with a diameter of 10 centimeters and a height of 20 centimeters rests on its circular base. It is cut in half horizontally. What is the difference between the combined surface areas of the two newly created cylinders and the total surface area of the original cylinder?
These are my choices:
a. 100rr sq cm
b. 50rr sq cm
c. 25rr sq cm
d. 0 sq cm
I came up with 100rr sq cm??
JESUS
big cylinder = 2π(5^2) + 2π(5)(20) = 300π
smaller = 2π(5^2) + 2π(5)(10) = 200π
but we have two of those, so the new surface area is 400π
difference is 100π
you are correct is the "rr" is supposed to be π
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of .)
To solve this problem, we need to calculate the surface areas of the two newly created cylinders and compare them to the total surface area of the original cylinder.
First, let's find the total surface area of the original cylinder.
The formula to calculate the surface area of a cylinder is 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.
Given that the diameter of the original cylinder is 10 centimeters, we can find the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 10 cm / 2 = 5 cm
Height (h) of the original cylinder = 20 cm
Now, let's calculate the surface area of the original cylinder:
Surface Area of the original cylinder = 2πr² + 2πrh
= 2π(5 cm)² + 2π(5 cm)(20 cm)
= 2π(25 cm²) + 2π(100 cm²)
= 50π cm² + 200π cm²
= 250π cm²
Now, let's consider the two newly created cylinders after cutting the original cylinder in half horizontally.
Each newly created cylinder has a height of 10 cm, which is half of the original cylinder's height, and the radius remains the same.
Surface Area of one newly created cylinder = 2πr² + 2πrh
= 2π(5 cm)² + 2π(5 cm)(10 cm)
= 2π(25 cm²) + 2π(50 cm²)
= 50π cm² + 100π cm²
= 150π cm²
Since we have two newly created cylinders, the combined surface area is twice the surface area of one newly created cylinder:
Combined Surface Area of two newly created cylinders = 2 * Surface Area of one newly created cylinder
= 2 * 150π cm²
= 300π cm²
Finally, we can calculate the difference between the combined surface areas of the two newly created cylinders and the total surface area of the original cylinder:
Difference = Combined Surface Area of two newly created cylinders - Surface Area of the original cylinder
= (300π cm²) - (250π cm²)
= 50π cm²
Therefore, the difference between the combined surface areas of the two newly created cylinders and the total surface area of the original cylinder is 50π cm².
As for the answer choices, 50π cm² can be simplified further. The value of π is approximately 3.14. So, 50 multiplied by 3.14 is equal to approximately 157.
Therefore, the correct answer is b. 50π sq cm, which is approximately 157 sq cm.