Question 1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2 m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution :
i) length = 10 cm, breadth = 12 cm, height = 14 cm
Given, the Length of cuboid = 10 cm
The Breadth of cuboid = 12 cm
The Height of cuboid = 14 cm
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(10 × 12 + 12 × 14 + 14 × 10) = 856 cm2
Hence, the surface area of given cuboid is 856 cm2
ii) length = 6 dm, breadth = 8 dm, height = 10 dm
Given, the Length of cuboid = 6 dm
The Breadth of cuboid = 8 dm
The Height of cuboid = 10 dm
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(6 × 8 + 8 × 10 + 10 × 6) = 376 dm2
Hence, the surface area of given cuboid is 376 dm2
iii) length = 2 m, breadth = 4 m, height = 5 m
Given, the Length of cuboid = 2 m
The Breadth of cuboid = 4 m
The Height of cuboid = 5 m
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(2 × 4 + 4 × 5 + 5 × 2) = 76 m2
Hence, the surface area of given cuboid is 76 m2
iv) length = 3.2 m, breadth = 30 dm, height = 250 cm
Given, the Length of cuboid = 3.2 m = 32 dm
The Breadth of cuboid = 30 dm
The Height of cuboid = 250 dm = 25 dm
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(32 × 30 + 30 × 25 + 25 × 32) = 5020 dm2
Hence, the surface area of given cuboid is 5020 dm2
Question 2. Find the surface area of a cube whose edge is
(i) 1.2 m
(ii) 27 cm
(iii) 3 cm
(iv) 6 m
(v) 2.1 m
Solution:
i) 1.2 m
Given, the Edge of cube = 1.2 m
And the Surface area of cube = 6 × edge2
= 6 × (1.2)2 = 8.64 m2
Hence, the surface area of a given cube is 8.64 m2
ii) 27 cm
Given, the Edge of cube = 27 cm
And the Surface area of cube = 6 × edge2
= 6 × (27)2 = 4374 cm2
Hence, the surface area of a given cube is 4374 cm2
iii) 3 cm
Given, the Edge of cube = 3 cm
And the Surface area of cube = 6 × edge2
= 6 × (3)2 = 54 cm2
Hence, the surface area of a given cube is 54 cm2
iv) 6 m
Given, the Edge of cube = 6 m
And the Surface area of cube = 6 × edge2
= 6 × (6)2 = 216 m2
Hence, the surface area of a given cube is 216 m2
v) 2.1 m
Given, the Edge of cube = 2.1 m
And the Surface area of cube = 6 × edge2
= 6 × (2.1)2 = 26.46 m2
Hence, the surface area of a given cube is 26.46 m2
Question 3. A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area?
Solution :
Given, the Length of cuboidal box = 5 cm
The Breadth of cuboidal box = 5 cm
The Height of the cuboidal box = 4 cm
And, Surface area of cuboidal box = 2(l × b + b × h + h × l)
= 2(5 × 5 + 5 × 4 + 4 × 5) = 130 cm2
Hence, the surface area of the given cuboidal box is 130 cm2
Question 4. Find the surface area of a cube whose volume is
(i) 343 m3
(ii) 216 dm3
Solution:
i) Given, the volume of cube = 343 m3
It means (side)3 = 343
So, side = 7 m
And, the Surface area of cube = 6 × side2
= 6 × (7)2 = 294 m2
Hence, the surface area of a given cube is 294 m2
ii) Given, the volume of cube = 216 dm3
It means (side)3 = 216
So, side = 6 dm
And, the Surface area of cube = 6 × side2
= 6 × (6)2 = 216 dm2
Hence, the surface area of a given cube is 216 dm2
Question 5. Find the volume of a cube whose surface area is
(i) 96 cm2
(ii) 150 m2
Solution:
i) Given, the surface area of cube = 96 cm2
It means 6 × side2 = 96
So, side = 4 cm
And, the Volume of cube = (side)3
= (4)3 = 64 cm3
Hence, the volume of the given cube is 64 cm3
ii) Given, the surface area of cube = 150 m2
It means 6 × side2 = 150
So, side = 5 m
And, the Volume of cube = (side)3
= (5)3 = 125 m3
Hence, the volume of the given cube is 125 m3
Question 6. The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions?
Solution:
Given, the dimensions of a cuboid are in the ratio 5 : 3 : 1
The total surface area is 414 m2
So, the Length of cuboid = 5a
The Breadth of cuboid = 3a
The Height of cuboid = 1a
And, Surface area of cuboid = 2(l × b + b × h + h × l)
414 = 2(5a × 3a + 3a × a + a × 5a)
414 = 46a2
So, a = 3 m
We can conclude, Length = 5a = 15 m
The Breadth = 3a = 9 m
The Height = a = 3 m
Hence, the dimensions of a cuboid are 15 m, 9 m, and 3 m.
Question 7. Find the area of the cardboard required to make a closed box of length 25 cm, 0.5 m, and height 15 cm?
Solution:
Given, the Length of Cuboidal cardboard = 25 cm
The Breadth of Cuboidal cardboard = 0.5 m = 50 cm
The Height of Cuboidal cardboard = 15 cm
Area of cardboard needed = Area of Cuboid
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(25 × 50 + 50 × 15 + 15 × 25) = 4750 cm2
Hence, the area of cardboard required is 4750 cm2
Question 8. Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 12 cm?
Solution :
Given, the Edge of cube = 12 cm
The surface area of a wooden box = Surface area of Cube
And, the Surface area of cube = 6 × edge2
= 6 × (12)2 = 864 cm2
Hence, the surface area of a wooden box is 864 cm2
Question 9. The dimensions of an oil tin are 26 cm× 26 cm× 45 cm. Find the area of the tin sheet required for making 20 such tins. If 1 square meter of the tin sheet costs Rs. 10, find the cost of the tin sheet used for these 20 tins?
Solution :
Given, the Length of oil tin = 26 cm
The Breadth of oil tin = 26 cm
The Height of oil tin = 45 cm
Area of tin sheet required to make 1 oil tin = Surface area of Cuboid
And, Surface area of cuboid = 2(l × b + b × h + h × l)
= 2(26 × 26 + 26 × 45 + 45 × 26) = 6032 cm2
And, Area of tin sheet required to make 20 oil tins = 20 × 6032 = 120640 cm2
= 12.064 m2
Since, 1 m2 Tin cost = Rs 10
So, 12.064 m2 Tin cost = Rs 10 × 12.064
= Rs 120.64
Hence, the area of tin required to make 20 oil tin is 12.064 m2 and the cost of making 20 oil tin is Rs 120.64
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