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Surface Area2020-12-31T19:08:11+10:00

Timetable › Forums › Standard › Measurement › Surface Area

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    Keymaster
    December 2, 2018 at 12:33 pm
    Post count: 1622
    #15000
    Surface Area
    Cube

    vol_cube

    $$SA=6s^2$$

     
    Rectangular Prism

    vol_rectangularprism

    $$SA=2LW+2LH+2WH$$

     
    Triangular Prism

    vol_triangularprism

    $$SA=2(\frac{1}{2}bh)+2sL+bL$$

     
    Pyramid

    vol_pyramid

    $$SA=LW+the\:sum\:of\: the\: 4\:triangles$$

     
    Cylinder

    vol_cylinder

    $$SA=2\pi r^2+2\pi rh$$

     
    Open Cylinder

    cylinder_sa2

    $$SA=2\pi r h$$

     
    Open One End Cylinder

    cylinder_sa1

    $$SA=\pi r^2+2\pi r h$$

     
    Cone

    vol_cone

    $$SA= \pi r^2+\pi rL$$

     
    Sphere

    vol_sphere

    $$SA=4\pi r^2$$
    Truncated Cone

    j_cone_0001

    $$SA=\pi\, R^2+\pi\,r^2+\pi\,R\,L-\pi\,r\,l$$

     
     
     
    Admin
    Keymaster
    December 2, 2018 at 1:36 pm
    Post count: 1622
    #15004

    A sphere has a radius of 10cm. Find:
    a. the surface area
    b. the volume

    a. Surface area = $$4\times\pi\times10^2$$
    = 1256.5cm2
    Use the surface area formula: $$4\pi r^2$$

    b. Volume = $$\frac43\pi\times 10^3$$
    = 4188.8cm3Use the volume formula: $$\frac43\pi r^3$$

    Admin
    Keymaster
    December 2, 2018 at 3:08 pm
    Post count: 1622
    #15009

    A cylinder, open at one end, has a radius of 10cm and a height of 15cm. Find the surface area.
    $$SA=\pi\times10^2+2\times\pi\times10\times20$$
    = 1570.80cm2

    Admin
    Keymaster
    December 31, 2020 at 7:08 pm
    Post count: 1622
    #18738

    Calculate the surface area of a closed hemisphere with a radius of 5cm. Answer correct to the nearest cm.

    Total surface area = half of the sphere plus the circular base

    SA = ½ × 4 × π × 52 + π × 52

    SA = 235.619

    = 236 cm2

    Admin
    Keymaster
    December 31, 2020 at 7:11 pm
    Post count: 1622
    #18739
    A cylinder, open at both ends, has a radius of 10cm and a height of 15cm. Find the surface area.
    $$SA=2\times\pi\times10\times20$$
    = 1256.64cm2    		 $$SA=2\pi r h$$ r = 10, h = 20
       
    a. V = 4/3 × π × 2.253
    = 47.7cm3    		 Use the volume formula for a sphere: $$V=\frac{4}{3}\pi r^3$$ and calculate, where r = ½ of the diameter 
    radius = ½ × 4.5 = 2.25
    b. 2 × 1 = 2 

    If it is 10cm wide, that means it can fit 2 balls across its width.
    2 × 1 × 6 = 12 balls If 5cm high, can only fit one ball.  so if we can fit two per row, and we need 12, so it has to be able to fit six rows along its length, 2 × 1 × 6 = 12 balls
    6 × 4.5 = 27cm now if each ball is 4.5cm in diameter, then 6 balls long to fit the 12, so 6 × 4.5 
    Admin
    Keymaster
    December 31, 2020 at 7:11 pm
    Post count: 1622
    #18741
    A sphere has a surface area of 200 cm2. Find the radius.

    SA = 200

    $$200 = 4\pi\;r^2$$

    		 divide both sides by 4$$\pi$$

    r2 = 15.915

    r = 3.99cm

    		 square root both sides
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