Surface Area of Shapes 3

Question 1 of 7

Find the surface area of the figure

$Surface Area =$ $\text(Surface Area )=$ (372) $m^{2}$ $\text(m)^2$

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Area of a Trapezium Formula

Area = \frac{1}{2} \times

$\text(Area)=1/2 times$ $height$ $\text(height)$

\times (

$times ($ ${base}_{1}$ $\text(base)_1$

+

$+$ ${base}_{2}$ $\text(base)_2$

)

$)$

Area of a Rectangle Formula

Area =

$\text(Area )=$ $length$ $\text(length)$

\times

$times$ $height$ $\text(height)$

Showing and Labelling the Surfaces

We need to add the areas of all the faces of the figure: the two trapezoids and the four rectangles

Next, solve for the area of the trapezoids using the Area of a Trapezium formula

Note that there are two trapezoids with the same lengths, so we will multiply this area by

2

$2$ for the surface area

$Area$ $\text(Area)$ _{$trapezoids$ $\text(trapezoids)$}	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $height$ $\text(height)$ $\times ($ $times ($ ${base}_{1}$ $\text(base)_1$ $+$ $+$ ${base}_{2}$ $\text(base)_2$ $)$ $)$

	$=$ $=$	$\frac{1}{2} \times$ $1/2 times$ $5$ $5$ $\times ($ $times ($ $10$ $10$ $+$ $+$ $14$ $14$ $)$ $)$ $=$ $=$ $60 m^{2}$ $60 \text(m)^2$

Now, solve for the area of the rectangles using the Area of a Rectangle formula

Note that there are two rectangles each with the same lengths, so we will multiply the first area by

2

$2$ for the surface area

$Area$ $\text(Area)$ _{$side rectangles$ $\text(side rectangles)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $height$ $\text(height)$
	$=$ $=$	$6$ $6$ $\times$ $times$ $7$ $7$ $=$ $=$ $42 m^{2}$ $42 \text(m)^2$

$Area$ $\text(Area)$ _{$upper rectangle$ $\text(upper rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $height$ $\text(height)$
	$=$ $=$	$10$ $10$ $\times$ $times$ $7$ $7$ $=$ $=$ $70 m^{2}$ $70 \text(m)^2$

$Area$ $\text(Area)$ _{$lower rectangle$ $\text(lower rectangle)$}	$=$ $=$	$length$ $\text(length)$ $\times$ $times$ $height$ $\text(height)$
	$=$ $=$	$14$ $14$ $\times$ $times$ $7$ $7$ $=$ $=$ $98 m^{2}$ $98 \text(m)^2$

Finally, add all the areas to find the surface area of the figure

$SA$ $\text(SA)$	$=$ $=$	$(2 \times$ $(2times$ $60$ $60$ $) + (2 \times$ $)+(2times$ $42$ $42$ $) +$ $)+$ $70$ $70$ $+$ $+$ $98$ $98$	Plug in the areas
$SA$ $\text(SA)$	$=$ $=$	$372 m^{2}$ $372 \text(m)^2$

The given measurements are in metres, so the area is measured as square metres

SA = 372 m^{2}

$\text(SA)=372 m^2$

Question 2 of 7

Find the surface area of the Hemisphere

Round your answer to

2

$2$ decimal places

Use

π = 3.141592654

$pi=3.141592654$

$Surface Area =$ $\text(Surface Area )=$ (35995.49, 35977.24, 36009.98) ${cm}^{2}$ $\text(cm)^2$

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Area of a Circle Formula

Area = π \times

$\text(Area)=pi times$ ${radius}^{2}$ $\text(radius)^2$

Surface Area of a Hemisphere

SA = \frac{1}{2} \times 4 \times π \times

$\text(SA )=1/2 times 4 times pi times$ ${radius}^{2}$ $\text(radius)^2$

Showing and Labelling the Surfaces

We need to add the areas of all the faces of the hemisphere: the flat circular part and the hemisphere itself

First, find the area of the top circular part using the formula for Area of a Circle

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$Area$ $\text(Area)$ _{$top part$ $\text(top part)$}	$=$ $=$	$π \times$ $pi times$ ${radius}^{2}$ $\text(radius)^2$
	$=$ $=$	$π \times$ $pi times$ ${61.8}^{2}$ $61.8^2$
	$=$ $=$	$11998.49633 {cm}^{2}$ $11998.49633 \text(cm)^2$

Next, use the formula to find the surface area of the hemisphere (half the formula for the Sphere)

Use

π = 3.141592654

$pi=3.141592654$ See

π

$pi$ explained

$SA$ $\text(SA)$ _{$hemisphere$ $\text(hemisphere)$}	$=$ $=$	$\frac{1}{2} \times 4 \times π \times$ $1/2 times 4 times pi times$ ${radius}^{2}$ $\text(radius)^2$

	$=$ $=$	$\frac{1}{2} \times 4 \times π \times$ $1/2 times 4 times pi times$ ${61.8}^{2}$ $61.8^2$

	$=$ $=$	$23996.99265 {cm}^{2}$ $23996.99265 \text(cm)^2$

Finally, add the areas to find the surface area of the figure

$SA$ $\text(SA)$	$=$ $=$	$11998.49633$ $11998.49633$ $+$ $+$ $23996.99265$ $23996.99265$	Plug in the areas
$SA$ $\text(SA)$	$=$ $=$	$35995.49 {cm}^{2}$ $35995.49 \text(cm)^2$	Rounded to two decimal places

The given measurements are in centimetres, so the area is measured as square centimetres

SA = 35995.49 {cm}^{2}

$\text(SA)=35995.49 \text(cm)^2$

The answer will depend on which

π

$pi$ you use.

In this solution we used:

π = 3.141592654

$pi=3.141592654$ .

Using	Answer
$π = 3.141592654$ $pi=3.141592654$	$35995.49 c m^{2}$ $35995.49 cm^2$
$π = 3.14$ $pi=3.14$	$35977.24 c m^{2}$ $35977.24 cm^2$
$π = \frac{22}{7}$ $pi=(22)/(7)$	$36009.98 c m^{2}$ $36009.98 cm^2$

Question 3 of 7

What is the surface area of this sphere?

Round your answer to

1

$1$ decimal place

Use

π \approx 3.14

$pi~~3.14$

Surface Area $=$ $=$ (452.2) $c m^{2}$ $cm^2$

Question 4 of 7

What is the surface area of this half sphere?

Round your answer to

2

$2$ decimal places

Use

π \approx 3.14

$pi~~3.14$

Surface Area $=$ $=$ (3052.08) $m m^{2}$ $mm^2$

Question 5 of 7

What is the surface area of this sphere?

Round your answer to

$1$ decimal place

Use

$pi~~3.14$

Surface Area $=$ (1017.4) $m^2$

Question 6 of 7

What is the surface area of this cylinder?

Round your answer to

$1$ decimal place

Use

$pi~~3.14$

Surface Area $=$ (1758.4) $mm^2$

Question 7 of 7

What is the surface area of this cylinder?

Round your answer to

$2$ decimal places

Use

$pi~~3.14$

Surface Area $=$ (2204.28) $mm^2$

$S A$ $SA$	$=$ $=$	$4 \times π \times {radius}^{2}$ $4 xx pi xx color(royalblue)(text(radius))^2$	Surface area of a sphere formula

	$=$ $=$	$4 \times 3.14 \times 6^{2}$ $4 xx 3.14 xx color(royalblue)(text(6))^2$	Plug in the known lengths

	$=$ $=$	$4 \times 3.14 \times 36$ $4 xx 3.14 xx 36$	Simplify
	$=$ $=$	$452.16$ $452.16$
	$=$ $=$	$452.2 c m^{2}$ $452.2 \ cm^2$	Rounded to 1 decimal place

$color(royalblue)(text(radius))$	$=$	$1/2 xx color(forestgreen)(18)$

$color(royalblue)(text(radius))$	$=$	$color(royalblue)(9)$

$SA$	$=$	$4 xx pi xx color(royalblue)(text(radius))^2$	Surface area of a sphere formula

	$=$	$4 xx 3.14 xx color(royalblue)(text(9))^2$	Plug in the known lengths

	$=$	$4 xx 3.14 xx 81$	Simplify
	$=$	$1,017.36$
	$=$	$1,017.4 \ m^2$	Rounded to 1 decimal place

$SA$	$=$	$2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$	Surface area of a cylinder formula

	$=$	$2 xx pi xx color(royalblue)(text(8))^2+2 xx pi xx color(royalblue)(\text(8)) xx color(darkviolet)(\text(27))$	Plug in the known lengths

	$=$	$2 xx 3.14 xx 64+2 xx 3.14 xx 8 xx 27$	Simplify
	$=$	$401.92+1356.48$
	$=$	$1,758.4 \ mm^2$	Rounded to 1 decimal place

$SA$	$=$	$2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$	Surface area of a cylinder formula

	$=$	$2 xx pi xx color(royalblue)(text(9))^2+2 xx pi xx color(royalblue)(\text(9)) xx color(darkviolet)(\text(30))$	Plug in the known lengths

	$=$	$2 xx 3.14 xx 81+2 xx 3.14 xx 9 xx 30$	Simplify
	$=$	$508.68+1695.6$
	$=$	$2,204.28 \ mm^2$	Rounded to 2 decimal places

Surface Area of Shapes 3

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Quiz summary

Information

1. Question

Hint

Fantastic!

Area of a Trapezium Formula

Area of a Rectangle Formula

Showing and Labelling the Surfaces

2. Question

Hint

Exceptional!

Area of a Circle Formula

Surface Area of a Hemisphere

Showing and Labelling the Surfaces

3. Question

Keep Going!

Surface Area of a Sphere

Labelling the given lengths

4. Question

Keep Going!

Area of a Circle Formula

Surface Area of a Hemisphere

5. Question

Keep Going!

Surface Area of a Sphere

Labelling the given lengths

6. Question

Keep Going!

Surface Area of a Cylinder

Labelling the given lengths

7. Question

Keep Going!

Surface Area of a Cylinder

Labelling the given lengths

Quizzes

$SA$ $\text(SA)$	$=$ $=$	$1, 017.36$ $1,017.36$ $+$ $+$ $2, 034.72$ $2,034.72$	Plug in the areas
$SA$ $\text(SA)$	$=$ $=$	$3, 052.08 {mm}^{2}$ $3,052.08 \text(mm)^2$	Rounded to two decimal places