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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

Respuesta :

frika
1. Sphere with a radius R=3 units has volume [tex]V_1= \frac{4}{3} \pi R^3=\frac{4}{3} \pi 3^3=36\pi[/tex];

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

4. Cone with a radius R=3 units and a height H=4 units has volume:
[tex]V_4= \frac{1}{3} \pi R^2\cdot H=\frac{1}{3} \pi 3^2\cdot 4=12\pi[/tex].

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


Edufirst
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


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

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