A large cylinder has a volume of about 5,400 cubic cm. A small cylinder is similar in shape to the larger cylinder with a scae factor of 2/3.Which measurement is closest to the volume of a cylinder.
f)1600cubic cm
g)2400 cubic cm
h)2700 cubic cm
j)3600 cubic cm
The answer is somehow f (1600 cubic cm)
but I need help on how to figure it out an explain it.
2/3 * 5400 = ?
To determine the volume of the small cylinder, we need to apply the scale factor of 2/3 to the volume of the larger cylinder.
The scale factor is applied to all three dimensions (length, width, and height) of the cylinders. Since volume is calculated by multiplying these three dimensions, we can say that the volumes of similar shapes are proportional to the cube of their scale factor.
Therefore, the volume of the small cylinder is equal to (2/3)³ times the volume of the large cylinder.
Given that the volume of the large cylinder is 5,400 cubic cm, we can now calculate the volume of the small cylinder.
Volume of small cylinder = (2/3)³ * 5,400
To calculate this, we multiply 5,400 by (2/3)³:
Volume of small cylinder = (2/3)³ * 5,400
= (8/27) * 5,400
= 1,600 cubic cm
Hence, the closest measurement to the volume of the small cylinder is option f) 1600 cubic cm.