1. A cone has a radius of 40 cm and a volume of 1875 cm^3. what is the volume of a similar cone with a radius of 16 cm.
A: 120 cm^3
B: 300 cm^3
C: 75 cm^3
D: 750^3
I know the answer is A but could someone explain how to do the problem.
volume is proportional to length cubed for similar geometry
2 times length is 4 times area
2 times length is 8 times volume
so
1875(16/40)^3 = 1875(.064) = 120cm^3
Thank you so much
Pretty much six years later... So who did you vote for president in 2020?
Number 13 what is the volume of a sphere with a radius of 4 m rounded to the nearest square
To find the volume of a sphere, we can use the formula:
V = (4/3) * π * r^3
Given that the radius (r) is 4 m, we can substitute it into the formula:
V = (4/3) * π * (4^3)
V = (4/3) * π * 64
V ≈ 268.08257
Rounding this volume to the nearest square, we get:
V ≈ 268 m^3
So, the volume of the sphere, rounded to the nearest square, is approximately 268 m^3.
To find the volume of a similar cone, you can use the property of similar figures that states that the ratio of their corresponding side lengths is equal to the ratio of their corresponding volumes, cubed.
First, find the ratio of the radii of the two cones: 16 cm / 40 cm = 0.4.
Next, find the ratio of their volumes: (0.4)^3 = 0.064.
Finally, multiply the given volume of 1875 cm^3 by the ratio of volumes to find the volume of the similar cone: 1875 cm^3 x 0.064 = 120 cm^3.
Therefore, the volume of the similar cone with a radius of 16 cm is 120 cm^3, which matches option A.