Question

Drag each statement to the correct location on the table. Classify the shapes based on their volumes. a cone with a radius of 12 units and a height of 6 units a cylinder with a diameter of 12 units and a height of 27 units a sphere with a diameter of 12 units a cylinder with a diameter of 8 units and a height of 18 units a sphere with a radius of 9 units a cone with a diameter of 18 units and a height of 36 units 288 TT 972 TT​

Answer 1

1. volume of cone = 288π cube units

2. volume of cylinder = 972π cube units

3. volume of sphere = 288π cube units

4. volume of cylinder = 288π cube units

5. volume of sphere = 972π cube units

6. volume of cone = 972π cube units

Answer 2

288
`\pi`

• cone with radius 12 and height 6
• cylinder with diameter 8 and height 18
• sphere with diameter 12

972
`\pi`

• cone with diameter 18 and height 36
• cylinder with diameter 12 and height 27
• sphere with radius 9

Explanation:

`\textsf{volume of a sphere} =\frac43\pi r^3`

`\textsf{volume of a cone} =\frac13\pi r^2h`

`\textsf{volume of a cylinder} =\pi r^2h`

`\textsf{diameter} =2r`

(where r is the radius, h is the height and d is the diameter)

Input the given values of r (d) and/or h into the above equations

Cone

r = 12, h = 6: volume = 288
`\pi`

d = 18 ⇒ r = 9, h = 36: volume = 972
`\pi`

Cylinder

d = 12 ⇒ r = 6, h = 27: volume = 972
`\pi`

d = 8 ⇒ r = 4, h = 18: volume = 288
`\pi`

Sphere

d = 12 ⇒ r = 6: volume = 288
`\pi`

r = 9: volume = 972
`\pi`