Answer: the first two figures, a sphere with a radius of three units, and a cone with a diameter of twelve units and a height of three units, have a volume equal to 36π
Step-by-step explanation:
You have to test each choice.
1) a sphere with a radius of three units
r = 3
Formula: Volume of a sphere, V = (4/3) π (r)³
Calculation:
V = (4/3)π (3)³ = 4×9π = 36π
∴ This is figure has the volume 36π
2) a cone with a diameter of twelve units and a height of three units
d = 12 ⇒ r = 12 / 2 = 6
h = 3
Formula: Volume of a cone, V = (1/3) π (r²) h
Calculations: V = (1/3) π (6²) (3) = 36 π
Conclusion: this solid has a volume equal to 36π
3) a cylinder with a diameter of six units and a height of one unit
d = 6 ⇒ r = 3
h = 1
Formula:
Volume of a cylinder, V = π r² h
Calculations: V = π(3²)(1) = 9π
∴ This solid does not have a volume of 36π
4) a cone with a radius of three units and a height of four units
r = 3
h = 4
Volume of the cone, V = (1/3)π (r²) h
Calculations: V = (1/3)π (3²) (4) = 12 π
Conclusion: this figure does not have a volume equal to 36π