The document discusses volume formulas and exercises for various 3D shapes: - Right prisms have a volume equal to the area of the base multiplied by the height. - Cylinders have a volume equal to pi multiplied by the radius squared and the height. - Cones have a volume equal to one third multiplied by pi multiplied by the radius squared and the height. - Pyramids have a volume equal to one third multiplied by the base area multiplied by the height. - Spheres have a volume equal to four thirds multiplied by pi multiplied by the radius cubed. The exercises provide example volume calculations and problems finding missing dimensions using the formulas.

1. Friday, January 25, 2013
SOLID GEOMETRY
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2. Friday, January 25, 2013
Volume of a right prism
Formula for Prism
Volume = base area x height
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3. Friday, January 25, 2013
Volume of a right prism
Given base area= 35cm2
8cm
Formula for Prism
Volume = base area x height
= 35 cm2 x 8 cm
= 280 cm3
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4. Friday, January 25, 2013
Exercise
 1. Find the volume of the given prisms.
 a. Base area = 40 cm 2 Height = 7 cm
 b. Base area = 34 cm 2 Height = 6 cm
 c. Base area = 47 cm 2 Height = 2.5 cm
 d. Base area = 79 cm 2 Height = 10.5 cm
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5. Friday, January 25, 2013
CYLINDER
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6. Friday, January 25, 2013
Volume of cylinder
Formula for Cylinder
Volume = base area x height
= π r2 h
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7. Friday, January 25, 2013
Volume of cylinder
Formula for Cylinder
7cm
Volume = base area x height
8cm = π r2 h
= 22 x 7 x 7 x 8
7
= 1232 cm3
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8. Friday, January 25, 2013
Exercise
 1. Find the volume of the given cylinder.
 a. Base area = 49 cm2 Height = 9 cm
 b. Base area = 34 cm2 Height = 7 cm
 c. Radius = 7 cm Height = 2.5 cm
 d. Radius = 49 cm Height = 10 cm
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9. Friday, January 25, 2013
Exercise
 2. Find the volume of the given cylinder.
 a. c.
Height = 7cm Radius = 7cm
Height = 2.4cm Radius = 7cm
d.
 b.
Height = 5.5cm Radius = 14cm
Height = 13cm Radius = 14cm
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10. Friday, January 25, 2013
CONE
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11. Friday, January 25, 2013
Volume of CONE
Formula for Cone
Volume = 1 x base area x height
3
= 1 π r2 h
3
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12. Friday, January 25, 2013
Exercise
 1. Find the volume of the given cone.
 a. Base area = 63 cm2 Height = 9 cm
 b. Base area = 72 cm2 Height = 7 cm
 c. Radius = 7 cm Height = 3 cm
 d. Radius = 49 cm Height = 15 cm
1a. Volume = (63 x 9 ) / 3 = 189cm3 1c. Volume = 1 x 22 x 7 x 7 x 3 = 154cm3
1b. Volume = (72 x 7 ) / 3 = 168 cm3 3 7
1d. Volume = 1 x 22 x 49 x 49 x 15 = 37730 cm3
3 7
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13. Friday, January 25, 2013
Exercise
 2. Find the volume of the given cone.
2b.
 a.
Height = 4cm Volume Cone= 1 x 22 x 7 x 7 x 14
Radius = 7cm
3 7
= 15092
2a.
21
Volume Cone= 1 x 22 x 7 x 7 x 4 b.
= 718.67cm3
3 7
= 4312
21 Height = 14cm Radius = 7cm
= 205.33cm3
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14. Friday, January 25, 2013
SOLID GEOMETRY
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15. Friday, January 25, 2013
PYRAMID
Formula for Volume of Pyramid
height
Volume = base area x height
3
width
Volume = length x width x h
length
3
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16. Friday, January 25, 2013
Exercise
 1. Find the volume of the given pyramid.
 a. Base area = 49 cm 2 Height = 9 cm
 b. Base area = 34 cm 2 Height = 7 cm
 c. Length =7 cm Width= 9cm Height = 2.5 cm
 d. Length =8 cm Width= 10cm Height = 6 cm
1a. Vpy= 49 x 9 = 147 cm3 1c. Vpy= 7 x 9 x2.5 = 52.5 cm3
3 3
1b. Vpy= 34 x 7 = 79.33 cm3 1d. Vpy= 8 x 10 x 6 = 160 cm3
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17. Friday, January 25, 2013
Exercise
 2. Find the volume of the given pyramid.
 a. b.
6 cm 8 cm
8cm 10cm
6cm 5cm
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18. Friday, January 25, 2013
SPHERE
Volume of Sphere
Volume = 4 π r3
3
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19. Friday, January 25, 2013
SPHERE
Volume = 4 π r3
3
7CM
= 4 X 22 X 7 X 7 X 7
3 7
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20. Friday, January 25, 2013
Exercise
 1. Find the volume of the given sphere.
 a. radius = 3.5cm Ans: 179.67cm 3
 b. radius = 2.1cm Ans: 38.81cm e. 3
 c. radius = 5 cm Ans: 523.81cm 3
8
 d.
3
Ans: 113.14cm3 Ans: 268.19cm3
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21. Friday, January 25, 2013
Finding the height
or the radius
of a cylinder.
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22. Friday, January 25, 2013
1. Finding the height or the radius of a cylinder.
a. The volume of a c. The volume of a
cylinder is 462 r=7cm h=16cm cylinder is 154
cm3. Find its cm3. Find its
radius if the height if the
height is 3 cm. radius is 7/4 cm.
b. The volume of a d. The volume of a
cylinder is 4400 cylinder is 1056
cm3. Find its cm3. Find its
h=1.714cm
radius if the height if the
height is 14 cm. r=10cm radius is 14 cm.
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23. Friday, January 25, 2013
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24. Friday, January 25, 2013
Finding the height
or the radius
of a cone.
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25. Friday, January 25, 2013
2. Finding the height or the radius of a cone.
a. The volume of a c. The volume of a
cone is 132 cm3. cone is 154 cm3.
Find its radius if the Find its height if the
height is 14 cm. radius is 7 cm.
b. The volume of a d. The volume of a
cone is 77 cm3. cone is 297 cm3.
Find its radius if the Find its height if the
height is 6 cm. radius is 9 cm.
2a. 3cm 2b. 3.5cm 2c. 3cm 2d. 3.5cm
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26. Friday, January 25, 2013
Finding the height,
length or width
of a pyramid.
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27. Friday, January 25, 2013
3. Finding the height or length or width of a pyramid.
c. The volume of a
a. The volume of a pyramid is 64 cm3.
pyramid is 180 cm3. Find its height if the
Find its height if the length is 4 cm and
base area is 60 cm2. the width is 8cm.
b. The volume of a d. The volume of a
pyramid is 40 cm3. pyramid is 40 cm3.
Find its height if the Find its length if the
base area is 20 cm2. height is 6 cm and
3a. 9cm 3b. 6cm the width is 4cm.
3c. 6cm 3d. 5cm
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28. Friday, January 25, 2013
VOLUME OF COMBINED
SOLID
BY
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Volume = volume of cylinder + volume of cone
Volume = πr2h + 1 πr2h
3cm
3
Volume = 22 x 7 x 7 x 10 + 1 x 22 x 7 x 7 x 3
7 3 7
Volume = 22 x 7 x 10 + 1 x 22 x 7
10cm Volume = 1540 + 154
Volume = 1694 cm3
14 cm
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30. Friday, January 25, 2013
Find the volume of the combined solid.
1. 8cm 2.
2cm
3cm
1232cm3
6cm
Radius=7cm
3cm
1334.67cm3
Radius=7cm
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31. Friday, January 25, 2013
Find the volume of the combined solid.
3. 2104.67cm3 2361.33cm3
4.
6cm
9cm
Radius=7cm Radius=7cm
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32. Friday, January 25, 2013
Find the volume of the combined solid.
5. 1026.67cm3
6. 9cm
2720.67cm3
10cm
6cm
Radius=7cm Diameter=14cm
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33. Friday, January 25, 2013
CONE
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34. Friday, January 25, 2013
CONE
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