Grade 8 Volume 1
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Transcript of Grade 8 Volume 1
1CONFIDENTIAL 1
Grade 8 Grade 8
Volume 1Volume 1
2
Solid Geometry
Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes
are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids.
The three flat shapes of the triangle, rectangle, and circle may become solids by adding the third dimension of depth. The triangle becomes a
cone; the rectangle, a rectangular solid; and the circle, a cylinder.
3
Cubes
A cube is a three-dimensional figure with all edges of the same length.
s s
s If s is the length of sides of the cube ,Volume of the cube = s3
Cuboids
l w
hIf l is the length, w is the width and h is the height of the cuboids ,Volume of the cuboids = lwh
4
Cylinders
A cylinder is a solid with two congruent circles joined by a curved surface.
In the given figure, the radius of the circular base is r and the height is h. The volume of the cylinder is the area of the base × height.
The volume of the cylinder =Πr2h.
r
h
Spheres
A sphere is a solid with all its points the same distance from the center.
rIf r is the length of radius of the sphere ,Volume of the sphere = 4Πr3
3
5
A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of
its base is perpendicular to the base. .
Cones
If r is the radius and h is the height, Volume of the cone = 1Πr2h
3
r
h
6
b b
hs
Regular square pyramid
Volume of the Regular square pyramid = 1b2h
3
7
Let us do some practice problems!
8CONFIDENTIAL
8
1) What is volume of the cube with length of sides = 7 cm?
a) 343 cm3
b) 345 cm3
c) 347 cm3
d) 349 cm3
9CONFIDENTIAL
9
2) What is the volume of the cuboid with length 7 cm, width 4 cm and height 6 cm.
a) 162 cm3
b) 164 cm3
c) 166 cm3
d) 168 cm3
10CONFIDENTIAL 10
3) What is the volume of the cylinder with radius of the base is 8 cm and the height is 10 cm? (Use Π = 3.14)
a) 2008.6 cm3
b) 2019.6 cm3
c) 2009.6 cm3
d) 2109.6 cm3
8cm
10cm
11CONFIDENTIAL 11
4) Which of the given boxes has the greatest volume?
a) Box Ab) Box Bc) Box Cd) All have equal volume
AB C
1ft4ft
2ft
3ft3ft
3ft6ft
2ft
2ft
12CONFIDENTIAL 12
5) This net can be folded on the dashed lines to make a box. What is the volume of the box?
a) 370 in3.b) 270 in3.c) 360 in3.d) 250 in3.
13CONFIDENTIAL
6) What is the volume of the sphere with radius = 6 cm? (Use Π = 3.14)
a) 904.32 cm3
b) 906.32 cm3
c) 908.32 cm3
d) 910.32 cm3
6cm
14CONFIDENTIAL 14
7) What is the volume of the cone with radius 6 cm and the height is = 12 cm? (Use Π = 3.14)
a) 442.16 cm3
b) 432.16 cm3
c) 462.16 cm3
d) 452.16 cm36cm
12
15CONFIDENTIAL 15
8) The rectangular prism at the right is made from centimeter cubes. What is the volume of the prism?
a) 88 cm3
b) 64 cm3
c) 48 cm3
d) 76 cm3
16CONFIDENTIAL 16
9) What is the volume of the regular square pyramid with base 11 cm and the height 12 cm?
a) 481 cm3
b) 483 cm3
c) 482 cm3
d) 484 cm3
11cm 11cm
12cm
17CONFIDENTIAL 17
10) What is the volume of a cone, if the diameter of the cone is 12.4 cm. and the height of the
cone is 30 cm ? (Use Π = 3.14)
a) 1205 cm3
b) 1206 cm3
c) 1207 cm3
d) 1208 cm3
12.4cm
30
18
Assessment
19CONFIDENTIAL
19
1) A metal cube of edge 9 cm is melted and formed into 2 smaller cubes. If the edge of one smaller cube is 6 cm,
what the side of the second smaller cube?
a) 6 cmb) 4 cmc) 7 cmd) 8 cm
20CONFIDENTIAL 20
2) Three cuboids of dimensions 2cm x 5cm x 7cm, 4cm x 4cm x 5cm and 2cm x 3cm x 11cm are melted and a
cube is formed. What is the side of the cube?
a) 8 cmb) 6 cmc) 7 cmd) 9 cm
21CONFIDENTIAL 21
3) What is the volume of the cylinder with radius of the base is 10 cm and the height is 13 cm?
a) 4082 cm3
b) 4084 cm3
c) 4086 cm3
d) 4088 cm3
10cm
13cm
22CONFIDENTIAL 22
4) What is the length of each edge of the box that is a perfect cube with volume 512 units3?
a) 6 unitsb) 5 unitsc) 8 unitsd) 7 units
23CONFIDENTIAL 23
5) What is the volume of the given rectangular pyramid?
a) 892 cm3
b) 972 cm3
c) 794 cm3
d) 772 cm3
24CONFIDENTIAL 24
6) What is the volume of the sphere with radius = 13 cm?
a) 9138.1 cm3
b) 9158.1 cm3
c) 9178.1 cm3
d) 9198.1 cm3
13cm
25CONFIDENTIAL 25
7) Which of the given boxes has the least volume?
a) Box Ab) Box Bc) Box Cd) All have equal volume
AB C
3ft5ft
4ft
4ft4ft
4ft5ft
3ft
3ft
26CONFIDENTIAL 26
8) What is the volume of the cone with radius 5 cm and the height is = 9 cm?
a) 235.5 cm3
b) 232.5 cm3
c) 237.5 cm3
d) 231.5 cm3
5 cm
9
27CONFIDENTIAL 27
9) What is the volume of the regular square pyramid with base 7 cm and the height 9 cm?
a) 143 cm3
b) 145 cm3
c) 147 cm3
d) 149 cm3
7cm 7cm
9 cm
28CONFIDENTIAL 28
10) What is the volume of the given box?
a) 42 cm3
b) 52 cm3
c) 92 cm3
d) 102 cm3
29
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