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Homework help with volumes?

Hello, I need help with these volume questions as I do not understand one bit of it.... hope you can help it will be much appreciated.

1. Find the surface area of a cuboid with

a) length = 56 mm, breath = 45 mm and height = 36 mm

b) length = 1.2 m, breadth= 75 cm and height = 60 cm

2. A rectangular box of tissues has dimensions 31 cm by 16 cm by 5 cm.

Calculate the surface area of the box.

3. Calculate the volume of:

a) a prism with cross-sectional area 1.4 cm2 and length 11 cm

b) a cylindrical coin with diameter 22 mm and thickness 3 mm.

4. The diagram shows a triangular prism ABCDEF

CAB = 90°, AB = 4 cm, BC= 5 cm, CA= 3 cm and BE= 16 cm.

a) Calculate the surface area of the p rism.

b) Calculate the volume of the prism.

5. The diagram represents a cylindrical well. It is 10 m deep and has a

diameter of 1.6 m.

a) (i) Write down the radius of the well.

(ii) Calculate the volume of the welL

b) The well is dug through rock. Every cubic metre of this rock has a

mass of 2.3 tonnes. Calculate the mass of the rock removed in

digging the welL

6. A manufacturer is making a batch of 800 plastic knitting needles.

Each needle is cylindrical in shape, with a diameter of 6 mm and a

length of 32 cm. Calculate the total volume of plastic used in making

these needles.

1 Answer

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  • Karl
    Lv 6
    8 years ago
    Favorite Answer

    1) The faces of a cuboid are rectangular.

    There are two faces bounded by length and breadth, two bounded by length and height, and two bounded by height and breadth.

    a) L x B = 56mm x 45mm = 2520mm^2 (square millimeters)

    L x H = 56mm x 36mm = 2016mm^2

    B x H = 45mm x 36mm = 1620mm^2

    Since there are two of each (top AND bottom, left AND right, front AND back) the surface area is twice the sum of each of these rectangles

    S = 2 x (2520 + 2016 + 1620) = 2 x 6156 = 12,312 mm^2

    b) L x B = 1200cm x 75cm = 90,000 cm^2

    L x H = 1200cm x 60cm = 72,000 cm^2

    B x H = 75cm x 60cm = 4500 cm^2

    S = 2 x (90,000 + 72,000 + 4500) = 333,000 cm^2

    2) Arbitrarily assign these numbers to L, H, and B and calculate from there.

    S = 2 x (31 x 16 + 31 x 5 + 16 x 5) = 2 x (496 + 155 + 80) = 1462 cm^2

    3) Volume = area times length = 1.4 x 11 = 15.4 cm^3

    4) We're given that the object is a triangular prism.

    The triangle is a right triangle since angle CAB is 90°.

    Legs AB and BC are given.

    AB, the leg adjacent to the 90° angle is 4 cm.

    BC, the hypotenuse is 5 cm.

    So leg AC must be 3 cm, forming a 3:4:5 triangle.

    The area of this triangle is 1/2 x 3 x 4 = 6 cm^2.

    The length of the prism is BE = 16 cm.

    Volume = area x length = 16 x 6 = 96 cm^3

    5) The radius is half the diameter: 0.8m.

    The volume of a cylinder is pi x r^2 x h = 3.1416 * 0.64 * 10 = 20.1m^3

    20.1 m^3 x 2.3 tonnes = 26.1 tonnes

    6) The volume of a cylinder is pi x r^2 x length = 3.1416 x 0.3^2 x 32

    (6 mm = 0.6 cm. r = 1/2 of 0.6 cm = 0.3 cm)

    V = 9.048 cm^3

    Total volume = 9.048 x 800 = 6438 cm^3

    1000 cm^3 = 1 liter, so the total volume of plastic is 6.438 liters.

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