Class 8 Maths Mensuration Solid Shapes

Solid Shapes

Many objects that we see in our day to day life like book, pencil box, ice cream cone, football and cylinder are three-dimensional objects (solid shapes). All these objects occupy some shape and have three dimensions- length, breadth and height or depth.

Some shapes have two or more than two identical (congruent) faces. For example the cylinder has congruent circular faces that are parallel to each other.

Surface area of Cube, Cuboids and Cylinder

The surface area of a solid is the sum of the areas of its faces.

Cube:

If each side of the cube is l, then total surface area = 6l2

Example: Let each side of the cube is 5 cm,

So, total surface area = 6 * 52 = 6 * 25 = 150 cm2

Cuboid:

Let h, l and b are the height, length and width of the cuboid respectively.

So, total surface area = 2 (h * l + b * h + b * l) = 2(lb + bh + hl)

Example: Let the height, length and width of the box shown above are 10 cm,

15 cm and 20 cm respectively.

Then the total surface area = 2 (10 * 15 + 15 * 20 + 10 * 20)

= 2 (150 + 300 + 200)

= 2 * 650

= 1300 m2

Cylinder:

Let r is the radius of circular region and h is the height of cylinder.

Then total surface area of cylinder = 2πr(h + r)

Problem: A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

Solution:

Given: Radius of cylindrical tank (r) = 7 m

Height of cylindrical tank (h) = 3 m

Total surface area of cylindrical tank = 2πr(h + r)

= 2 * 22/7 * 7(3 + 7)

= 44 * 10

= 440 m2

Hence, 440 m2 metal sheet is required.

Volume of Cube, Cuboids and Cylinder

Amount of space occupied by a three dimensional object is called its volume.

Cube:

The cube is a special case of a cuboid, where l = b = h.

Hence, volume of cube = l * l * l = l3

Problem: Find the volume of cube if its each side is of length is 5 cm.

Solution:

Given, l = b = h = 5 cm

volume of cube = l * b * h = 5 * 5 * 5 = 125 cm3

Cuboid:

Volume of a cuboid is equal to the product of length, breadth and height of the cuboid.

Let l is the length, b is the breadth and h is the height of the cuboid.

Then volume of cuboid = l * b * h

Problem: Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?

Solution:

Given: Base area of cuboid = 180 cm2 and Volume of cuboid = 900 cm3

We know that, Volume of cuboid = l * b * h

=> 900 = 180 * h                                                          [Base area = l * b = 180 (given)]

=> h = 900/180

=> h = 5 m

Hence, the height of cuboid is 5 m.

Cylinder:

Let r is the radius of circular region and h is the height of cylinder.

Then volume of cylinder = πr2 * h = πr2h

Problem: Find the height of the cylinder whose volume if 1.54 m3 and diameter of the base is 140 cm.

Solution:

Given: Volume of cylinder = 1.54 m3 and Diameter of cylinder = 140 cm

Radius (r) = 140/2 = 70 cm

Volume of cylinder = πr2 h

=> 1.54 = 22/7 * 0.7 * 0.7 * h

=> 1.54 = 22 * 0.1 * 0.7 * h

=> 1.54 = 1.54 * h

=> h = 1.54/1.54

=> h = 1 m

Hence, the height of the cylinder is 1 m.

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