Answer :
Sure! Here are the answers to the questions provided:
a) To find the capacity of the cylindrical can, you can use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height of the cylinder. Given that the radius is 3.5 cm and the height is 12 cm, you can substitute these values into the formula:
V = π(3.5)^2(12) = π(12.25)(12) = 147π cm^3
Therefore, the capacity of the can is 147π cubic centimeters.
b) If the dimensions of the radius and height are switched, the new volume can be calculated using the same formula:
V' = π(12)^2(3.5) = π(144)(3.5) = 504π cm^3
Comparing the original volume with the switched dimensions volume:
Original volume: 147π cm^3
Switched dimensions volume: 504π cm^3
The capacity of the can increases significantly when the dimensions are switched because the volume of a cylinder is directly proportional to the square of the radius and the height. So, when you increase the radius and decrease the height (or vice versa), the volume increases due to the larger base area created by the radius change.
