Question

Which of the following solid figures have a volume of 36π cubic units? Select all that apply. a sphere with a radius of three units a cone with a diameter of twelve units and a height of three units a cylinder with a diameter of six units and a height of one unit a cone with a radius of three units and a height of four units

Answer 1

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

Answer 2

1. Sphere with a radius R=3 units has volume
`V_1= (4)/(3) \pi R^3=(4)/(3) \pi 3^3=36\pi`;

2. Cone with a diameter D=12 units and a height H=3 units has volume:
`V_2= (1)/(3) \pi R^2\cdot H=(1)/(3) \pi ( (D)/(2) )^2\cdot H=(1)/(3) \pi 6^2\cdot 3=36\pi`;
3. Cylinder with a diameter D=6 units and a height H=1 unit has volume:
`V_3=\pi R^2\cdot H=\pi ( (D)/(2) )^2\cdot H=\pi 3^2\cdot 1=9\pi`;

4. Cone with a radius R=3 units and a height H=4 units has volume:

`V_4= (1)/(3) \pi R^2\cdot H=(1)/(3) \pi 3^2\cdot 4=12\pi`.

Hence in first and second parts you obtain the volume equal to 36π and in third and fourth not equal.