1CONFIDENTIAL 1

Grade 8 Grade 8

Volume 1Volume 1

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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.

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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

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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

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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

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r

h

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b b

hs

Regular square pyramid

Volume of the Regular square pyramid = 1b2h

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Let us do some practice problems!

8CONFIDENTIAL

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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

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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

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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

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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

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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

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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

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Assessment

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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

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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

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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

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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

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5) What is the volume of the given rectangular pyramid?

a) 892 cm3

b) 972 cm3

c) 794 cm3

d) 772 cm3

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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

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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

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