Mathematics, 27.05.2021 23:10 Jenifermorales101

Find the surface area of the composite figure

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Answer from: livleluve76

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 from: kyliegriffis

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft 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 widthl is lengthh is height

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

r is radiush 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

[Surface Area of a Cylinder Formula] Factor: $\displaystyle SA = 2(\pi rh + \pi r^2)$ [Surface Area of a Cylinder Formula] Divide by 2 [Semi-Cylinder]: $\displaystyle SA = \pi rh + \pi r^2$ [Surface Area of a Semi-Cylinder] Substitute in r [Radius Formula]: $\displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d}{2})^2$ [Surface Area of a Semi-Cylinder] Evaluate exponents: $\displaystyle SA = \pi (\frac{d}{2})h + \pi (\frac{d^2}{4})$ [Surface Area of a Semi-Cylinder] Multiply: $\displaystyle SA = \frac{\pi dh}{2} + \frac{\pi d^2}{4}$ [Surface Area of a Rectangular Prism] Remove top: $\displaystyle SA = 2(wh + lh) + lw$ 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

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

Answer from: Quest

The percent discount was 120

Answer from: Quest

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