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  1. Asked: In:

    The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.

    Best Answer
    amitpaswan09

    Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m Volume of cylindrical wooden pipe = π(R² - r²)h = 22/7 × (14² - 12²) × 35 = 22 × (196 - 144 ) × 5 = 22 × 52 × 5 = 5720 cm³ Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³Read more

    Inner radius of cylindrical pipe r = 24/2 = 12 cm, outer radius R = 28/2 = 14 cm and lenght h = 35 m
    Volume of cylindrical wooden pipe = π(R² – r²)h
    = 22/7 × (14² – 12²) × 35 = 22 × (196 – 144 ) × 5 = 22 × 52 × 5 = 5720 cm³
    Mass of cylindrical wooden pipe = 5720 × 0.6 g = 3432 g = 3.432 kg [∵ 1 cm³ of wood has a mass of 0.6 g]
    Hence, the volume of cylindrical wooden pipe is 3.432 kg.

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  2. Asked: In:

    A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

    Best Answer
    amitpaswan09

    Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm Volume of tin can = lbh = 5 × 4 × 15 = 300 cm³ Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm Volume of plastic cylinder = πr²H 22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³ Difference between capacities of tRead more

    Length of tin can l = 5 cm, breadth b = 4 cm and height h = 15 cm
    Volume of tin can = lbh = 5 × 4 × 15 = 300 cm³
    Radius of plastic cylinder r = 7/2 = 3.5 cm and height H = 10 cm
    Volume of plastic cylinder = πr²H
    22/7 × 3.5 × 3.5 × 10 = 22 × 0.5 × 3.5 × 10 = 385 cm³
    Difference between capacities of two packs = 385 – 300 = 85 cm³
    Hence, the capacity of plastic cylindrical pack is greater than tin can by 85 cm³.

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  3. Asked: In:

    If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base. (ii) its volume. (Use π= 3.14)

    Best Answer
    amitpaswan09

    (I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm. Let, the radius of cylinder = r cm Lateral surface area of cylinder C = 2πrh ⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm Hence, the radius of base is 3 cm. (II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³Read more

    (I) Lateral surface area of cylinder C = 94.2 cm² and height h = 5 cm.
    Let, the radius of cylinder = r cm
    Lateral surface area of cylinder C = 2πrh
    ⇒ 94.2 = 2 × 3.14 × r × 5 ⇒ r = (94.2)/(3.14×10) = 3 cm
    Hence, the radius of base is 3 cm.
    (II) Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³
    Hence, the volume of cylinder is 141.3 cm³.

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  4. Asked: In:

    It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m², find

    Best Answer
    amitpaswan09

    (I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m. Let, the inner radius of cylindrical vessel = r m The inner curved surface area of cylindrical vessel = 2πrh The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh According to question, RsRead more

    (I) Cost of painting the inner curved surface of cylindrical vessel = Rs 2200 and height h = 10 m.
    Let, the inner radius of cylindrical vessel = r m
    The inner curved surface area of cylindrical vessel = 2πrh
    The cost of painting is at the rate of Rs 20 per m² = Rs 20 × 2πrh
    According to question, Rs 20 × 2πrh = 2200
    ⇒ 2πrh = 2200/20 = 110
    Hence, the inner curved surface area is 110 m².

    (II) The inner curved surface area of cylindrical vessel = 2πrh
    ⇒ 110 = 2 × 22/7 × r × 10 ⇒ r = 110×7/22×2×10 = 7/4 = 1.75 m
    Hence, the radius of base of cylindrical vessel is 1.75 m.

    (III) Volume of cylindrical cessel = πr²h
    = 22/7 × 1.75 × 1.75 × 10 = 22 × 0.25 × 1.75 × 10 = 96.25 m³
    Hence, the volume of cylindrical vessel is 96.25 m³.

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  6. Asked: In:

    The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of metal sheet would be needed to make it?

    Best Answer
    amitpaswan09

    Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m Let, the radius of cylindrical vessel = r m Volume of cylindrical vessel V = πr²h ⇒ 0.0154 = 22/7 r²× 1 ⇒ r² = 0.0154 × 7/22 = 0.0049 ⇒ r = √0.0049 = 0.07 m Total surface area of cylindrical vessel = 2πr(r +hRead more

    Capacity of cylindrical vessel V = 15.4 litres = 15.4/1000m³ = 0.0154 m³ and height h = 1 m
    Let, the radius of cylindrical vessel = r m
    Volume of cylindrical vessel V = πr²h
    ⇒ 0.0154 = 22/7 r²× 1
    ⇒ r² = 0.0154 × 7/22 = 0.0049
    ⇒ r = √0.0049 = 0.07 m
    Total surface area of cylindrical vessel = 2πr(r +h)
    = 2 × 22/7 × 0.07 × (0.07 + 1) = 2 × 22 × 0.01 × 1.07 = 0.4708 m²
    Hence, 0.4708 m² metal sheet is required to make this cylindrical vessel.

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