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katen-ka-za [31]
3 years ago
7

Find the surface area of the composite figure

Mathematics
2 answers:
nataly862011 [7]3 years ago
8 0

solution given:

For Cuboid

length[l]=11mm

breadth [b]=9mm

height[h]=6mm

For semi cylinder

height[H]=11mm

radius[r]=\frac{9}{2}=4.5mm

Now

Totalsurface area=2(lb+bh+lh)+½(2πr(r+H))-l*b[/tex]

:2(11*9+9*6+11*6)+22/7*4.5(4.5+11)-11*9

:438+219.2-99

:558.2mm²

Here area of base is subtracted as it is not included.

<u>T</u><u>o</u><u>t</u><u>a</u><u>l</u><u> </u><u>s</u><u>u</u><u>r</u><u>f</u><u>a</u><u>c</u><u>e</u><u> </u><u>a</u><u>r</u><u>e</u><u>a</u><u> </u><u>o</u><u>f</u><u> </u><u>c</u><u>o</u><u>m</u><u>p</u><u>o</u><u>s</u><u>i</u><u>t</u><u>e</u><u> </u><u>f</u><u>i</u><u>g</u><u>u</u><u>r</u><u>e</u><u> </u><u>i</u><u>s</u><u> </u><u>:</u><u>5</u><u>5</u><u>8.</u><u>2</u><u>mm²</u><u>.</u>

skad [1K]3 years ago
6 0

Answer:

\displaystyle SA_{Total} = \frac{279 \pi}{4} + 339 \ mm^2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Factoring

<u>Geometry</u>

Shapes

Congruency

  • Congruent sides and lengths

Radius Formula: \displaystyle r = \frac{d}{2}

  • <em>d</em> is diameter

Surface Area of a Rectangular Prism Formula: SA = 2(wl + hl + hw)

  • <em>w</em> is width
  • <em>l</em> is length
  • <em>h</em> is height

Surface Area of a Cylinder Formula: SA = 2πrh + 2πr²

  • <em>r</em> is radius
  • <em>h</em> is height

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

[Rectangular Prism] <em>w</em> = 9 mm

[Rectangular Prism] <em>l</em> = 11 mm

[Rectangular Prism] <em>h</em> = 6 mm

[Cylinder] <em>d</em> = 9 mm

[Cylinder] <em>h</em> = 11 mm

<u>Step 2: Derive</u>

<em>Modify Surface Area equations and combine</em>

  1. [Surface Area of a Cylinder Formula] Factor:                                                 \displaystyle SA = 2(\pi rh + \pi r^2)
  2. [Surface Area of a Cylinder Formula] Divide by 2 [Semi-Cylinder]:              \displaystyle SA = \pi rh + \pi r^2
  3. [Surface Area of a Semi-Cylinder] Substitute in <em>r</em> [Radius Formula]:             \displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d}{2})^2
  4. [Surface Area of a Semi-Cylinder] Evaluate exponents:                                \displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d^2}{4})
  5. [Surface Area of a Semi-Cylinder] Multiply:                                                    \displaystyle SA = \frac{\pi dh}{2} + \frac{\pi d^2}{4}
  6. [Surface Area of a Rectangular Prism] Remove top:                                      \displaystyle SA = 2(wh + lh) + lw
  7. Combine Surface Area equations:                                                                  \displaystyle SA_{Total} = \frac{\pi dh}{2} + \frac{\pi d^2}{4} + 2(wh + lh) + lw

<u>Step 3: Find Surface Area</u>

  1. Substitute in variables [Combined Surface Area equation]:                         \displaystyle SA_{Total} = \frac{\pi (9 \ mm)(11 \ mm)}{2} + \frac{\pi (9 \ mm)^2}{4} + 2[(9 \ mm)(6 \ mm) + (11 \ mm)(6 \ mm)] + (11 \ mm)(9 \ mm)
  2. Evaluate exponents:                                                                                         \displaystyle SA_{Total} = \frac{\pi (9 \ mm)(11 \ mm)}{2} + \frac{\pi (81 \ mm^2)}{4} + 2[(9 \ mm)(6 \ mm) + (11 \ mm)(6 \ mm)] + (11 \ mm)(9 \ mm)
  3. Multiply:                                                                                                            \displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 2[54 \ mm^2 + 66 \ mm^2] + 99 \ mm^2
  4. [Brackets] Add:                                                                                                 \displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 2[120 \ mm^2] + 99 \ mm^2
  5. Multiply:                                                                                                            \displaystyle SA_{Total} = \frac{99\pi \ mm^2}{2} + \frac{81\pi \ mm^2}{4} + 240 \ mm^2 + 99 \ mm^2
  6. Add:                                                                                                                   \displaystyle SA_{Total} = \frac{279 \pi}{4} + 339 \ mm^2
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