Wednesday, June 8, 2022 AIRIL BIN AHMAD SOLID GEOMETRY
NOTE MATH FORM 3 - SOLID GEOMETRY
Jun 20, 2015
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Thursday, April 13, 2023
AIRIL BIN AHMAD
SOLID GEOMETRY
AIRIL BIN AHMAD
Thursday, April 13, 2023
Volume of a right prism
Formula for Prism
Volume = base area x height
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
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
CYLINDER
AIRIL BIN AHMAD
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Volume of cylinder
Formula for Cylinder
Volume = base area x height
= π r2 h
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
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
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE
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
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
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
SOLID GEOMETRY
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
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
AIRIL BIN AHMAD
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Exercise
2. Find the volume of the given pyramid. a. b.
6 cm
8cm6cm
8 cm
10cm
5cm
AIRIL BIN AHMAD
Thursday, April 13, 2023
SPHERESPHERE
Volume of Sphere
Volume = 4 π r3
3
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
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height or the radius
of a cylinder.
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height or the radius
of a cone.
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
Finding the height, length or width
of a pyramid.
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
Thursday, April 13, 2023
AIRIL BIN AHMAD
VOLUME OF COMBINED SOLID
BY
AIRIL BIN AHMAD
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
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
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
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
AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE
AIRIL BIN AHMAD
Thursday, April 13, 2023
CONE
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