Total Surface Area of Cube
A cube is a solid object having six square faces of equal
length (l). Area of each square face is l2. Therefore the total
surface area (TSA) of a cube is 6l2.
There are 12 edges in a cube. Therefore, the perimeter of
a cube is 12l, and the latreal surface area (LSA) i.e. area of 4 faces (walls) is 4l2.
Volume of cube = l3
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Net of a Cube
Net of a cube is as given below:
Workout Examples
Example 1: Find the total surface area of the given solid figure.
Solution: The given solid
figure is a cube of length (l) 8cm,
∴ T.S.A. of cube = 6l2
= 6 × (8cm)2
= 6 × 64 cm2
= 384 cm2
Example 2: The total surface area of a cubical box is 216cm2.
Find the length of the box.
Solution: Here,
T.S.A. of cubical box = 216cm2
i.e. 6l2 = 216
or, l2 = 216/6
or, l2 = 36
or, l = 6cm
Example 3: If the volume of cubical block is 1728cm3,
Find:
a. The length of its each edge.
b. The total surface area of the block.
c. The cost of painting its all edges at Rs. 50 per cm2.
Solution: Here,
Volume of cubical block = 1728cm3
i.e. l3 = 1728
or, l = 12cm
a. ∴ length of each edge = 12cm
b. ∴ T.S.A. of block = 6l2
= 6 × (12cm)2
= 6 × 144cm2
= 864cm2
c. Rate of painting = Rs. 50
per cm2
∴ Cost of painting =
Rate × Area
= Rs. 50 × 864
= Rs. 43200
You can comment your questions or problems
regarding area and volume of cubes here.
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