.length = 15 m, breadth = 6 m and height = 9 dm
length = 22 cm, breadth = 12 cm and height = 7.5 cm
length = 48 cm, breadth = 6 dm and height = 1 m
length = 24 m, breadth = 25 cm and height = 6 m
Answers
Answer:
Given Length=22cm, breadth=12cm and height=7.5cm
We know that volume of cuboid= length × breadth × height
V = (22 × 12 × 7.5)
V = 1980cm3
We know that total surface area of cuboid= 2(l b + b h + h l)
Surface area = 2 (22 × 12 + 12 × 7.5 + 7.5 × 22)
Surface area = 2 (264 + 165 + 90)
Total Surface area = 1038cm2
We know that lateral area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(22 + 12) × 7.5]
Lateral surface area = 510 cm2
(ii) Given Length=15m, breadth=6m and height=9m
We know that volume of cuboid= length × breadth × height
V = (15 × 6 × 0.9)
V = 81m3
We know that total surface area of cuboid= 2(l b + b h + h l)
Surface area = 2 (15 × 6 + 6 × .9 + .9 × 15)
Surface area = 2 (90 + 13.5 + 5.4)
Total Surface area = 217.8m2
We know that lateral surface area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(15 + 6) × 0.9]
Lateral surface area = 37.8 m2
(iii) Given Length=24m, breadth=25cm and height=6m
We know that volume of cuboid= length × breadth × height
V = (24 × 0.25 × 6)
V = 36m3
We know that total surface area of cuboid= 2(lb + b h + hl)
Surface area = 2 (24 × .25 + .25 × 6 + 6 × 24)
Surface area = 2 (6 + 155 + 1.5)
Total Surface area = 303m2
We know that lateral area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(24 + .25) × 6]
Lateral surface area = 291 m2
Rs aggarwal solutions
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Mathematics
Chapters in Mathematics class 8th RS Aggarwal
Exercises in Volume and Surface Area of Solids
Question 1
Find the volume, lateral surface area and the total surface area of the cuboid whose
dimensions are:
(i) Length=22cm, breadth=12cm and height=7.5cm
(ii) Length=15m, breadth=6m and height=9dm
(iii) Length=24m, breadth=25cm and height=6m
(iv) Length=48cm, breadth=6dm and height=1m
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(i) Given Length=22cm, breadth=12cm and height=7.5cm
We know that volume of cuboid= length × breadth × height
V = (22 × 12 × 7.5)
V = 1980cm3
We know that total surface area of cuboid= 2(l b + b h + h l)
Surface area = 2 (22 × 12 + 12 × 7.5 + 7.5 × 22)
Surface area = 2 (264 + 165 + 90)
Total Surface area = 1038cm2
We know that lateral area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(22 + 12) × 7.5]
Lateral surface area = 510 cm2
(ii) Given Length=15m, breadth=6m and height=9m
We know that volume of cuboid= length × breadth × height
V = (15 × 6 × 0.9)
V = 81m3
We know that total surface area of cuboid= 2(l b + b h + h l)
Surface area = 2 (15 × 6 + 6 × .9 + .9 × 15)
Surface area = 2 (90 + 13.5 + 5.4)
Total Surface area = 217.8m2
We know that lateral surface area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(15 + 6) × 0.9]
Lateral surface area = 37.8 m2
(iii) Given Length=24m, breadth=25cm and height=6m
We know that volume of cuboid= length × breadth × height
V = (24 × 0.25 × 6)
V = 36m3
We know that total surface area of cuboid= 2(lb + b h + hl)
Surface area = 2 (24 × .25 + .25 × 6 + 6 × 24)
Surface area = 2 (6 + 155 + 1.5)
Total Surface area = 303m2
We know that lateral area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(24 + .25) × 6]
Lateral surface area = 291 m2
(iv) Given Length=48cm, breadth=6dm and height=1m
We know that volume of cuboid= length × breadth × height
V = (0.48 × 0.6 × 1)
V = 0.288m3
We know that total surface area of cuboid= 2(l b + b h + h l)
Surface area = 2 (0.48 × 0.6 + 0.6 × 1 + 1 × 0.48)
Surface area = 2 (.288 + 0.6 + 0.48)
Total Surface area = 2.736m2
We know that lateral surface area of cuboid= 2 [(l + b) × h]
Lateral surface area = 2 [(0.48 + 0.6) × 1]
Lateral surface area = 2.16 m2
Step-by-step explanation:
Thanks
Answer:
(i) We know that, Volume of cuboid = Length × Breadth × Height = (22 × 12 × 7.5) = 1980 cm3 We also know that, Total Surface Area of cuboid = 2 (lb + bh + hl) = 2 (22 × 12) + (22 × 7.5) + (12 × 7.5) = 2 (264 + 165 + 90) = 1038 cm2 Now, Read more on Sarthaks.com - https://www.sarthaks.com/1144718/i-length-22-cm-breadth-12-cm-and-height-7-5-cm-ii-length-15-m-breadth-6-m-and-height-9-dmLateral surface area of cuboid = [2 (l + b) × h] = 2 (22 + 12) × 7.5 = 510 cm2 (ii) We know that, Volume of cuboid = Length × Breadth × Height = (15 × 6 × 0.9) = 81 m3 We also know that, Total Surface Area of cuboid = 2 (lb + bh + hl) = 2 (15 × 6) + (15 × 0.9) + (6 × 0.9) = 2 (90 + 13.5 + 5.4) = 217.8 m2 Now, Lateral surface area of cuboid = [2 (l + b) × h] = 2 (15 + 6) × 0.9 = 37.8 m2 (iii) We know that, Volume of cuboid = Length × Breadth × Height = (24 × 0.25 × 6) = 36 m3 We also know that, Total Surface Area of cuboid = 2 (lb + bh + hl) = 2 (24 × 0.25) + (24 × 6) + (0.25 × 6) = 2 (6 + 144 + 1.5) = 303 m2 Now, Lateral surface area of cuboid = [2 (l + b) × h] = 2 (24 + 0.25) × 6 = 291 m2 (iv) We know that, Volume of cuboid = Length × Breadth × Height = (0.48 × 0.6 × 1) = 0.288 m3 We also know that, Total Surface Area of cuboid = 2 (lb + bh + hl) = 2 (0.48 × 0.6) + (0.48 × 1) + (0.6 × 1) = 2 (0.288 + 0.48 + 0.6) = 2.736 m2 Now, Lateral surface area of cuboid = [2 (l + b) × h] = 2 (0.48 + 0.6) × 1 = 2.16 m2Read more on Sarthaks.com - https://www.sarthaks.com/1144718/i-length-22-cm-breadth-12-cm-and-height-7-5-cm-ii-length-15-m-breadth-6-m-and-height-9-dm