Scottish Church College B.ED Department (2013-14) e-book
NAME-PARNA DEY ROLL NO- T-077 Subject – Mathematics Topic- cuboid and cube Class- IX 1
Content Page No. Cuboids & general cuboids
3
Rectangular cuboids & examples of cuboids
4
Total surface area of cuboids
5
Volume of cuboids
6
Diagonal of cuboids
7
Cube
8
Examples of cube
9
Total surface area of a cube
10- 11
Volume of cube
12
Diagonal of cube
13
Word problems
14- 19
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Cuboids .
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While some mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism,or rectangular parallelepiped
General cuboids By Euler's formula the number of faces ('F'), vertices (V), and edges (E) of any convex polyhedron are related by the formula "F + V " = E + 2 . In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges.
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Rectangular cuboids In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism. The term "rectangular or oblong prism" is ambiguous. Also the term rectangular parallelepiped or orthogonal parallelepiped is us
Examples of cuboids
4
Total surface area of a cuboids
The total surface area (TSA) of a cuboid is the sum of the areas of its six faces. That is:
TSA=2(lw+ wh+ hl)
5
Volume of a cuboids A cuboid with length l units, width w units and height h units has a volume of V cubic units given by:
V= l × w × h Example: Lengths in meters (m):
The volume is: 10 m × 5 m × 4 m = 200 m3 It also works out the same like this: 4 m × 5 m × 10 m = 200 m3
Note: the result is in m3 (cubic meters) because we have multiplied meters together three times.
6
Diagonal of a cuboids
Example: Lengths in centimeters (cm): alculate the diagonal of a cuboid with a length of 10 cm, width of 4 cm and height of 5 cm.
7
Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids.
8
Examples of Cube
9
Total surface area of a cube
10
Example: when s= 4:
11
Volume of a cube Recall that a cube has all edges the same length (See Cube definition). The volume of a cube is found by multiplying the length of any edge by itself twice.
volume = s3
Example: Lengths in centimeters (cm):
12
Diagonal of a cube
Space diagonal= √ 3 x Face diagonal= √ 2 x
where x= length of the sides
Example: Lengths in centimeters (cm): The value of the space diagonal of a unit cube is= √ 3 The value of the face diagonal of a unit cube is= √ 2
13
Maths is fun: solve these
Word Problem 1 What is the unknown edge of each of the cuboids below? a) Volume = 600 cm3
b) Volume = 4500 cm3
c) Volume = 6750 cm3
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Word Problem 2
The volume of the Rubik's cube below is 216 cm3. What is the length of one edge of the cube?
Word Problem 3 A rectangular container with a base area of 200 cm2 is filled with water to a height of 15 cm. If the container has a height of 20 cm, how much water (in litres) should be added to it to fill it completely?
15
Word Problem 4 Josh built a rectangular cardboard box 18 cm high with a square base and a volume of 2178 cm3. Then he realized he did not need a box that large, so, he chopped off the height of the box reducing its volume to 1331 cm3. Was the new box cubical?
Word Problem 5 A rectangular juice dispenser has a base area of 450 cm2 and a height of 25 cm. Gale adds syrup and water in the ratio 1 : 3 to the dispenser to make a beverage. If he uses 6.75 litres of water, what percentage of the dispenser will be filled when the beverage is made?
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Word Problem 6 A rectangular aquarium is
the aquarium is
2 filled. When 16 litres of water are added, 5
2 filled. Find the height of the aquarium if its length 3
and width are 50 cm and 40 cm respectively.
Word Problem 7 The water level in a rectangular tank 65 cm long and 45 cm wide is 14 cm. It will take another 58.5 litres of water to fill the tank to its brim. Find the height of the tank.
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Word Problem 8 Containers A (6 cm, 5cm, 4cm), B (5 cm, 4 cm, 3 cm) and C (3 cm, 3 cm, 2 cm) are three rectangular containers. At first, Container A is filled with water to its brim while containers B and C are empty. Next, some water from Container A is poured into containers B and C so that Container B is completely full while Container C is half full. Find the height of the water left in Container A.
Word Problem 9 A rectangular vase with a square base and 25 cm height is filled with water to its maximum capacity of 1.6 litres. Shelly puts some marbles into the vase causing 235 ml of water to spill. Then she removes all the marbles from the vase causing a further spillage of 85 ml of water. What is the height of the water level in the vase now?
18
Word Problem 10 An empty rectangular bath tub 150 cm long, 60 cm wide and 50 cm high is being filled with water from a tap at a rate of 30 litres per minute. The tap is turned off after 12 minutes. Water is then drained out of the tub at a rate of 18 litres per minute. What would be the drop in the water level (measured in cm) 6 mintues later?
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Notes:-
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