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Post a LessonAnswered on 02/02/2024 Learn CBSE - Class 8/Maths/Mensuration
Pooja R. Jain
The total surface area (AtotalAtotal) of a cuboid can be found using the formula:
Atotal=2(lw+lh+wh)Atotal=2(lw+lh+wh)
where:
Given that the length (ll) is 20 cm, breadth (ww) is 15 cm, and height (hh) is 10 cm, substitute these values into the formula:
Atotal=2(20×15+20×10+15×10)Atotal=2(20×15+20×10+15×10)
Atotal=2(300+200+150)Atotal=2(300+200+150)
Atotal=2(650)Atotal=2(650)
Atotal=1300 cm2Atotal=1300cm2
Therefore, the total surface area of the given cuboid is 1300 cm21300cm2.
Answered on 02/02/2024 Learn CBSE - Class 8/Maths/Mensuration
Pooja R. Jain
To find the cost of painting the curved surface area of all the cylindrical pillars, we'll first calculate the total curved surface area and then multiply it by the cost per square meter.
The curved surface area (AcurvedAcurved) of a cylindrical pillar is given by the formula:
Acurved=2πrhAcurved=2πrh
where:
Given that the radius (rr) is 28 cm and the height (hh) is 4 m (convert to cm: 4 m=400 cm4m=400cm), we can calculate the curved surface area of one pillar:
Acurved=2π×28×400Acurved=2π×28×400
Acurved=2×22/7×28×400Acurved=2×22/7×28×400
Now, calculate the total curved surface area for 24 pillars:
Total Curved Surface Area=24×AcurvedTotal Curved Surface Area=24×Acurved
Once you have the total curved surface area, multiply it by the cost per square meter to find the total cost:
Total Cost=Total Curved Surface Area×Cost per square meterTotal Cost=Total Curved Surface Area×Cost per square meter
Total Cost=(Total Curved Surface Area)×8 Rs/m2Total Cost=(Total Curved Surface Area)×8Rs/m2
Calculate these values to find the cost of painting the curved surface area of all the pillars.
Answered on 02/02/2024 Learn CBSE - Class 8/Maths/Mensuration
Pooja R. Jain
The total surface area (AtotalAtotal) of a cylinder is given by the formula:
Atotal=2πr(r+h)Atotal=2πr(r+h)
where:
Given that the radius (rr) is 7 cm and the total surface area (AtotalAtotal) is 968 cm², we can set up the equation:
968=2π×7×(7+h)968=2π×7×(7+h)
Now, solve for hh:
968=2×227×7×(7+h)968=2×722×7×(7+h)
968=44×(7+h)968=44×(7+h)
Divide both sides by 44:
22=7+h22=7+h
Now, solve for hh:
h=15h=15
Therefore, the height of the cylinder is 15 cm.
Answered on 02/02/2024 Learn CBSE - Class 8/Maths/Mensuration
Pooja R. Jain
To find the area of the paper needed to cover the base, side faces, and back faces of the cuboid, we need to calculate the total surface area.
The formula for the total surface area (TSA) of a cuboid is given by:
TSA=2(lw+lh+wh)TSA=2(lw+lh+wh)
where:
In this case, the dimensions of the cuboid are given as:
Substitute these values into the formula:
TSA=2(80×30+80×40+30×40)TSA=2(80×30+80×40+30×40)
TSA=2(2400+3200+1200)TSA=2(2400+3200+1200)
TSA=2×6800TSA=2×6800
TSA=13600 cm2TSA=13600cm2
Therefore, the area of the paper needed to cover the base, side faces, and back faces of the cuboid is 13600 cm213600cm2.
Answered on 02/02/2024 Learn CBSE - Class 8/Maths/Mensuration
Pooja R. Jain
Let's denote the hollow cylinder's outer radius as RR, inner radius as rr, and height as hh.
The lateral surface area (LSA) of a hollow cylinder is given by the formula: LSA=2πh(R+r)LSA=2πh(R+r)
In this case, the LSA is given as 4224 cm²: 4224=2πh(R+r)4224=2πh(R+r)
Now, the rectangular sheet is formed by cutting along the height of the hollow cylinder. The width of the rectangular sheet is given as 33 cm.
The width of the rectangular sheet is equal to the height of the hollow cylinder (hh). Therefore, h=33h=33 cm.
Now, we can rearrange the formula for LSA to find R+rR+r: R+r=LSA2πhR+r=2πhLSA
Substitute the given values: R+r=42242π×33R+r=2π×334224
Now, to find the perimeter of the rectangular sheet, we use the formula: Perimeter=2(Length+Width)Perimeter=2(Length+Width)
Since the width is given as 33 cm, and the length is equal to the outer circumference of the hollow cylinder, we find the outer circumference using C=2πRC=2πR: Length=2πRLength=2πR
Substitute the values and calculate: Length=2π×(42242π×33)Length=2π×(2π×334224)
Now, plug the values into the perimeter formula: Perimeter=2(2π×(42242π×33)+33)Perimeter=2(2π×(2π×334224)+33)
Simplify to get the numerical value. Keep in mind that ππ is approximately 3.14 for calculation purposes.
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