NOTE MATH FORM 3 - SOLID GEOMETRY
Transcript of NOTE MATH FORM 3 - SOLID GEOMETRY
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Thursday, April 13, 2023
AIRIL BIN AHMAD
SOLID GEOMETRY
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of a right prism
Formula for Prism
Volume = base area x height
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of a right prism
Formula for Prism
Volume = base area x height
= 35 cm2 x 8 cm
= 280 cm3
Given base area= 35cm2
8cm
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise1. Find the volume of the given prisms.a. Base area = 40 cm2 Height = 7 cmb. Base area = 34 cm2 Height = 6 cmc. Base area = 47 cm2 Height = 2.5 cmd. Base area = 79 cm2 Height = 10.5 cm
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AIRIL BIN AHMAD
Thursday, April 13, 2023
CYLINDER
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of cylinder
Formula for Cylinder
Volume = base area x height
= π r2 h
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of cylinder
Formula for Cylinder
Volume = base area x height
= π r2 h8cm
7cm
= 22 x 7 x 7 x 8
7
= 1232 cm3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
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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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise2. Find the volume of the given cylinder.a.
b.
Radius = 7cmHeight = 7cm
Radius = 14cmHeight = 13cm
Radius = 7cmHeight = 2.4cm
c.
d.
Radius = 14cmHeight = 5.5cm
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AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of CONE
Formula for Cone
Volume = 1 x base area x height
3
= 1 π r2 h
3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
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
1b. Volume = (72 x 7 ) / 3 = 168 cm3
1c. Volume = 1 x 22 x 7 x 7 x 3 = 154cm3
3 71d. Volume = 1 x 22 x 49 x 49 x 15 = 37730 cm3 3 7
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise 2. Find the volume of the given cone. a.
b.
Radius = 7cmHeight = 4cm
Radius = 7cmHeight = 14cm
2a.
Volume Cone= 1 x 22 x 7 x 7 x 4
3 7
= 4312
21
= 205.33cm3
2b.
Volume Cone= 1 x 22 x 7 x 7 x 14
3 7
= 15092
21
= 718.67cm3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
SOLID GEOMETRY
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AIRIL BIN AHMAD
Thursday, April 13, 2023
PYRAMIDPYRAMID
Formula for Volume of Pyramid
Volume = base area x height
3
Volume = length x width x h
3length
height
width
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise1. Find the volume of the given pyramid.a. Base area = 49 cm2 Height = 9 cmb. Base area = 34 cm2 Height = 7 cmc. Length =7 cm Width= 9cm Height = 2.5 cmd. Length =8 cm Width= 10cm Height = 6 cm
1a. Vpy= 49 x 9 = 147 cm3
3
1b. Vpy= 34 x 7 = 79.33 cm3
3
1c. Vpy= 7 x 9 x2.5 = 52.5 cm3
31d. Vpy= 8 x 10 x 6 = 160 cm3
3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise
2. Find the volume of the given pyramid. a. b.
6 cm
8cm6cm
8 cm
10cm
5cm
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Thursday, April 13, 2023
SPHERESPHERE
Volume of Sphere
Volume = 4 π r3
3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
SPHERESPHERE
Volume = 4 π r3
3
= 4 X 22 X 7 X 7 X 7
3 7
7CM
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Exercise1. Find the volume of the given sphere.a. radius = 3.5cmb. radius = 2.1cmc. radius = 5 cm d.
3
8
e.
Ans: 179.67cm3
Ans: 113.14cm3
Ans: 38.81cm3
Ans: 523.81cm3
Ans: 268.19cm3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height or the radius
of a cylinder.
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AIRIL BIN AHMAD
Thursday, April 13, 2023
1. Finding the height or the radius of a cylinder.
a. The volume of a cylinder is 462 cm3. Find its radius if the height is 3 cm.
b. The volume of a cylinder is 4400 cm3. Find its radius if the height is 14 cm.
c. The volume of a cylinder is 154 cm3. Find its height if the radius is 7/4 cm.
d. The volume of a cylinder is 1056 cm3. Find its height if the radius is 14 cm.
r=7cm
r=10cm
h=16cm
h=1.714cm
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AIRIL BIN AHMAD
Thursday, April 13, 2023
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height or the radius
of a cone.
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AIRIL BIN AHMAD
Thursday, April 13, 2023
2. Finding the height or the radius of a cone.
a. The volume of a cone is 132 cm3. Find its radius if the height is 14 cm.
b. The volume of a cone is 77 cm3. Find its radius if the height is 6 cm.
c. The volume of a cone is 154 cm3. Find its height if the radius is 7 cm.
d. The volume of a cone is 297 cm3. Find its height if the radius is 9 cm.
2a. 3cm 2b. 3.5cm 2c. 3cm 2d. 3.5cm
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AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height, length or width
of a pyramid.
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AIRIL BIN AHMAD
Thursday, April 13, 2023
3. Finding the height or length or width of a pyramid.
a. The volume of a pyramid is 180 cm3. Find its height if the base area is 60 cm2.
b. The volume of a pyramid is 40 cm3. Find its height if the base area is 20 cm2.
c. The volume of a pyramid is 64 cm3. Find its height if the length is 4 cm and the width is 8cm.
d. The volume of a pyramid is 40 cm3. Find its length if the height is 6 cm and the width is 4cm.3a. 9cm 3b. 6cm
3c. 6cm 3d. 5cm
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Thursday, April 13, 2023
AIRIL BIN AHMAD
VOLUME OF COMBINED SOLID
BY
AIRIL BIN AHMAD
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Thursday, April 13, 2023
AIRIL BIN AHMAD
Volume = volume of cylinder + volume of cone
Volume = πr2h + 1 πr2h
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
Volume = 1540 + 154
Volume = 1694 cm3
14 cm
10cm
3cm
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Thursday, April 13, 2023
AIRIL BIN AHMAD
Radius=7cm
8cm 2cm
Find the volume of the combined solid.
1.
6cm
3cm
3cm
Radius=7cm
2.
1334.67cm3
1232cm3
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Thursday, April 13, 2023
AIRIL BIN AHMAD
Radius=7cm
9cm
Find the volume of the combined solid.
3.
6cm
Radius=7cm
4.2104.67cm3 2361.33cm3
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Thursday, April 13, 2023
AIRIL BIN AHMAD
Radius=7cm
6cm
Find the volume of the combined solid.
5.
10cm
Diameter=14cm
6. 9cm1026.67cm3
2720.67cm3
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AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE
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AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE