The area of a cylinder’s base is 706.5 square millimeters. the cylinder’s lateral area is 471 square

The area of a cylinder's base is 706.5 square millimeters. the cylinder's lateral area is 471 square millimeters. what is the total surface area of the cylinder, in square centimeters?

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  1. 260/4 = 65 square inches is area of a side 
    area of a side = base*height/2 = base *13/2

    65 = b*13/2

    130=b*13

    b = 10 so the side length equal 10 inches 

    area of base = 10*10 = 100 

    volume of a pyramid = area of base time height /3 

    (the height of pyramid)^2 = 13^2 - 5^2

    h^2 = 169 -25 = 144 

    h = 12 

    V = area of base time height /3 = 100*12/3 = 400 cubic inches 

    hope this will help you 

  2. 5.5 inches

    Step-by-step explanation:

    Since it is a hexagon, there is 6 faces. The total lateral area is 6 times area of one face. The area of one face is 12 times the width so the total is 6*12*width which equals 396. Dividing both sides by 6 gives you 12*width = 66. Dividing both sides by 12 gives you width = 5.5.

  3. The slant height of the pyramid is [tex]9\ in[/tex]

    Step-by-step explanation:

    we know that

    The lateral area of the square base pyramid is equal to

    [tex]LA=4(\frac{1}{2}(b)(L))[/tex]

    where

    b is the length side of the base

    L is the slant height of the pyramid

    we have

    [tex]LA=270\ in^{2}[/tex]

    [tex]b=15\ in[/tex]

    substitute the values and solve for L

    [tex]270=4(\frac{1}{2}(15)(L))[/tex]

    [tex]270=30(L)[/tex]

    [tex]L=270/30=9\ in[/tex]

  4. Volume cylinder = 24501.42 m³

    The surface area of the cone = 151.5 in²

    The lateral area of the square pyramid = 352 in²

    Step-by-step explanation:

    ∵ The volume of the cylinder = area base × height

    ∵ Its base is a circle

    ∴ V = πr² × h = 3.14 × (34/2)² × 27 = 24501.42 m³

    ∵ The surface area of the cone = 1/2 perimeter base ×  Slant height + area base

    ∵ Its base is a circle

    ∴ S.A = (1/2) × 2πr × l + πr²

    ∵ The slant height = [tex]\sqrt{7^{2}+(\frac{8}{2})^{2}} =\sqrt{65}[/tex]

    ∴ S.A = 3.14 × (8/2) × √65 + 3.14 × (8/2)² = 151.5 in²

    ∵ The lateral area of the square pyramid = 1/2 perimeter base × slant height

    ∵ Its base is a square

    ∴ L.A = 1/2 × (8 × 4) × 22 = 352 in²

  5. 11.2

    Step-by-step explanation:

    The base of a lampshade is a regular hexagon with a height of 12 inches for each lateral face. The lateral area is 396 square inches. Determine the length of each side of the base

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