Sphere worksheet

1. Volume: 550.93 cubic units

1. The surface area is 4π times the radius squared, so divide the area by 4π to get r²

   $r^2$$=\frac{325}{4\pi }$$=25.862678$

2. Take the square root to undo the squaring and find the radius

   $r$$=\sqrt{25.862678}$$=5.085536$

3. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 5.085536$$=10.171072$

4. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 5.085536$$=31.953366$

5. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {5.085536}^3$$=550.933086$

2. Volume: 696.91 cubic units

1. The radius is half the diameter, so divide by 2

   $r$$=\frac{11}{2}$$=5.5$

2. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 5.5$$=34.557519$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times {5.5}^2$$=380.132711$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {5.5}^3$$=696.90997$

3. Volume: 332.38 cubic units

1. The distance around is 2π times the radius, so divide the circumference by 2π to get the radius

   $r$$=\frac{27}{2\pi }$$=4.297183$

2. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4.297183$$=8.594367$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times {4.297183}^2$$=232.047907$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {4.297183}^3$$=332.384143$

4. Volume: 268.08 cubic units

1. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4$$=8$

2. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 4$$=25.132741$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times 4^2$$=201.06193$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times 4^3$$=268.082573$

5. Volume: 179.59 cubic units

1. The radius is half the diameter, so divide by 2

   $r$$=\frac{7}{2}$$=3.5$

2. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 3.5$$=21.991149$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times {3.5}^2$$=153.93804$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {3.5}^3$$=179.59438$

6. Volume: 440.57 cubic units

1. The surface area is 4π times the radius squared, so divide the area by 4π to get r²

   $r^2$$=\frac{280}{4\pi }$$=22.281692$

2. Take the square root to undo the squaring and find the radius

   $r$$=\sqrt{22.281692}$$=4.720349$

3. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4.720349$$=9.440697$

4. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 4.720349$$=29.658826$

5. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {4.720349}^3$$=440.56588$

7. Volume: 488.6 cubic units

1. The surface area is 4π times the radius squared, so divide the area by 4π to get r²

   $r^2$$=\frac{300}{4\pi }$$=23.873241$

2. Take the square root to undo the squaring and find the radius

   $r$$=\sqrt{23.873241}$$=4.886025$

3. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4.886025$$=9.77205$

4. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 4.886025$$=30.699801$

5. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {4.886025}^3$$=488.602512$

8. Radius: 4.75

1. The volume is 4/3 × π times the radius cubed, so multiply by 3 and divide by 4π to get r³

   $r^3$$=\frac{3\times 450}{4\pi }$$=107.429587$

2. Take the cube root to undo the cubing and find the radius

   $r$$=\text{∛}107.429587$$=4.753804$

3. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4.753804$$=9.507609$

4. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 4.753804$$=29.869033$

5. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times {4.753804}^2$$=283.983081$

9. Volume: 351.19 cubic units

1. The distance around is 2π times the radius, so divide the circumference by 2π to get the radius

   $r$$=\frac{27.5}{2\pi }$$=4.376761$

2. The diameter goes all the way across, so it is twice the radius

   $d$$=2\times 4.376761$$=8.753522$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times {4.376761}^2$$=240.721851$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times {4.376761}^3$$=351.193999$

10. Volume: 904.78 cubic units

1. The radius is half the diameter, so divide by 2

   $r$$=\frac{12}{2}$$=6$

2. The distance around the widest part is 2π times the radius

   $C$$=2\times \pi \times 6$$=37.699112$

3. The surface area is 4π times the radius squared

   $A$$=4\times \pi \times 6^2$$=452.389342$

4. The volume is 4/3 × π times the radius cubed

   $V$$=\frac{4}{3}\times \pi \times 6^3$$=904.778684$