4. Find the expression for the sum of the edges of a cuboid with length I, breadth b and height h. Find the
perimeter of the six faces of the cuboid in terms of l, b, and h. How many faces of the cuboid have the sam
perimeter?
of the six faces of a cube having side b. How many faces in term of l, b, h
Answers
Answer:
The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is given by:
TSA = 2 (lw + wh + hl)
Remember the surface area is the total area of all the faces of a 3D shape.
The lateral surface area of a cuboid is given by:
LSA = 2 (lh + wh) = 2 h (l + w)
Example 1: Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.
TSA = 2 (lw + wh + hl)
TSA = 2 (8*6 + 6*5 + 5*8)
TSA = 2 (48 + 30 + 40)
TSA = 236
So, the total surface area of this cuboid is 236 cm2.
Example 2: Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm and 7.2 cm.
Solution:
Area of Face 1: 4.8 × 7.2 = 34.56 cm²
Area of Face 2: 3.4 × 7.2 = 24.48 cm²
Area of Face 3: 4.8 × 3.4 = 16.32 cm²
Adding the area of these 3 faces gives 75.36 cm², since each face is duplicated on the opposite side, the total surface area of the cuboid will be:
TSA = 2 (75.36) = 150.72 cm²
Example 3: The length, width and height of a cuboid are 10cm, 8cm and 7cm respectively. Find the lateral surface area of a cuboid.
Solution:
Lateral surface area of cuboid is given by:
LSA = 2h(l+w)
where,
l = length = 10 cm
w = width = 8 cm
h = height = 7 cm
Insert these values into the formula we will get:
LSA = 2 ×7(10 + 8)
LSA = 14 × 18
LSA = 252 cm2
Example 4: The length, breadth and height of a cuboid are 16cm, 14cm and 10cm respectively. Find the total surface area of the cuboid.
Solution:
The total surface area of a cuboid is given by:
TSA = 2 (l*b + b*h + h*l)
Given that:
l = 16cm
b = 14cm
h = 10cm
Substituting the values in the equation we will get
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(224 + 140 + 160)
TSA = 2 * 524
TSA = 1048 cm2
Example 5: Given a cereal box whose length is 20 cm, height is 30 cm and width is 8 cm. Find the surface area of the box.
Solution:
To find the surface are of the box we need to find the area of each rectangular face and add them all up.
The area of the front face is: 20 x 30 = 600 cm2.
The area of the top face is: 20 x 8 = 160 cm2.
The area of the side face is: 8 x 30 = 240 cm2.
Now add these values together we will get: 600 + 160 + 240 = 1000 cm2.
And the total surface area is therefore 1000 x 2 = 2000 cm2.
Example 6: Find the surface area of a cuboid whose sides are 3cm by 6cm by 10cm.
Solution:
Surface area of the cuboid is given by:
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(3 x 6 + 6 x 10 + 3 x 10)
TSA = 2(18 + 60 + 30)
TSA = 216 cm2
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