Question

Find the surface area of the composite figure

Answer 1

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.

Total surface area of composite figure is :558.2mm².

Answer 2

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Factoring

Geometry

Shapes

Congruency

• Congruent sides and lengths

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

• d is diameter

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

• w is width
• l is length
• h is height

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

• r is radius
• h is height

Step-by-step explanation:

Step 1: Define

Identify

[Rectangular Prism] w = 9 mm

[Rectangular Prism] l = 11 mm

[Rectangular Prism] h = 6 mm

[Cylinder] d = 9 mm

[Cylinder] h = 11 mm

Step 2: Derive

Modify Surface Area equations and combine

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 r [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:                                                                  $\displaystyle SA_{Total} = \frac{\pi dh}{2} + \frac{\pi d^2}{4} + 2(wh + lh) + lw$

Step 3: Find Surface Area

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