Home/ manvi zoon/Best Answers
  1. Asked: In:

    A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

    manvi zoon

    Radius of hemispherical part = radius of cylindrical part (r) = 3.5 cm Height of cylindrical part (h) = 10 m The total surface area of article = CSA of cylindrical part + CSA of two hemispherical part = 2πrh + 2 × 2πr² = 2π × 3.5 × 10 + 2 × 2π × 3.5 ×3.5 = 70π + 49π = 119π = 119 × (22/7) = 17 × 22 =Read more

    Radius of hemispherical part = radius of cylindrical part (r) = 3.5 cm
    Height of cylindrical part (h) = 10 m
    The total surface area of article
    = CSA of cylindrical part + CSA of two hemispherical part
    = 2πrh + 2 × 2πr²
    = 2π × 3.5 × 10 + 2 × 2π × 3.5 ×3.5
    = 70π + 49π = 119π
    = 119 × (22/7) = 17 × 22 = 374 cm²
    Hence, the total surface area of the article is 374 cm²

    See less
    • 1
  2. Asked: In:

    A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of p.

    manvi zoon

    Height of conical part (h) = dadius of conical part (r) = 1 cm Radius of conical part (r) = radius of hemispherical part (r) = 1 cm Volume of Solid = Volume of conical part + volume of hemispherical part = 1/3πr²h + 2/3πr³ = 1/3π. 1² . 1 + 2/3π. 1³ = πcm³

    Height of conical part (h) = dadius of conical part (r) = 1 cm
    Radius of conical part (r) = radius of hemispherical part (r) = 1 cm
    Volume of Solid = Volume of conical part + volume of hemispherical part
    = 1/3πr²h + 2/3πr³
    = 1/3π. 1² . 1 + 2/3π. 1³ = πcm³

    See less
    • 1
  3. Asked: In:

    Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

    manvi zoon

    Height of conical part (h₁) = 2 cm Radius of conical part (r) = Radius of cylindrical part (r) = 3/2 cm Height of cylindrical part (h₂) = 12 - 2 × Height of conical part = 12 - 2 × 2 = 8 cm The volume of air contained in the modal = Volume of cylindrical part + 2 × Volume of conical part = πr²h₂ + 2Read more

    Height of conical part (h₁) = 2 cm
    Radius of conical part (r) = Radius of cylindrical part (r) = 3/2 cm
    Height of cylindrical part (h₂) = 12 – 2 × Height of conical part
    = 12 – 2 × 2 = 8 cm
    The volume of air contained in the modal
    = Volume of cylindrical part + 2 × Volume of conical part
    = πr²h₂ + 2 × 1/3πr²h₁
    = π(3/2)² . 8 + 2 × 1/3π(3/2)².2
    = 18π + 3π = 21π = 21 × 22/7 = 66 cm³.

    See less
    • 1
  4. Asked: In:

    A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm

    manvi zoon

    Radium of hemispherical part (r) = Radius of cylindrical part (r) = 2.8/2 = 1.4 cm Height of Hemispherical part = Radius of hemispherical part = 1.4 cm Height of cylindrical part (h2) = 5 -2 × height of hemispherical part = 5 - 2 × 1.4 = 2.2 cm Volume of 1 Gulab jamun = Volume of cylindrical part +Read more

    Radium of hemispherical part (r) = Radius of cylindrical part (r) = 2.8/2 = 1.4 cm
    Height of Hemispherical part = Radius of hemispherical part = 1.4 cm
    Height of cylindrical part (h2) = 5 -2 × height of hemispherical part = 5 – 2 × 1.4 = 2.2 cm
    Volume of 1 Gulab jamun = Volume of cylindrical part + 2 × Volume of hemispherical part.
    = πr²h + 2 × 2/3πr³ = πr²h + 4/3πr³
    = π(1.4)² (2.2) + 4/3π(1.4)³
    = 22/7 × 1.4 × 1.4 × 2.2 + 4/3 × 22/7 × 1.4 × 1.4 × 1.4
    = 13.552 + 11.498
    = 25.05 cm³

    Volume of 45 Gulab Jamun
    = 45 × 25.5
    = 1,127.25 cm³
    Volume of sugar syrup = 30% of volume of 45 Gulab Jamun
    = 30/100 × 1127.25
    = 338.17 cm³

    See less
    • 1
  6. Asked: In:

    A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of ` 500 per m2. (Note that the base of the tent will not be covered with canvas.)

    manvi zoon

    Height of cylindrical part (h) = 2.1 m Diameter of cylindrical part = 4 m Radius of cylindrical part (r) = 2 m Height of conical part (l) = 2.8 m Area of convas used = CSA conical part + CSA of cylindrical part = πrl + 2πrh = π × 2 × 2.8 + 2π × 2 × 2.1 = 2π(2.8 + 4.2) = 2 × (22/7) × 7 = 44m² The CosRead more

    Height of cylindrical part (h) = 2.1 m
    Diameter of cylindrical part = 4 m
    Radius of cylindrical part (r) = 2 m
    Height of conical part (l) = 2.8 m
    Area of convas used = CSA conical part + CSA of cylindrical part
    = πrl + 2πrh
    = π × 2 × 2.8 + 2π × 2 × 2.1
    = 2π(2.8 + 4.2) = 2 × (22/7) × 7 = 44m²
    The Cost of 1 m² canvas = Rs500
    Therefore, the cost of 44m² canvas = 44 × Rs.500 = Rs.22000.

    See less
    • 1