Surface Area of Shapes 2
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Question 1 of 7
1. Question
Find the surface area of the figureRound your answer to two decimal places `\text(Surface Area )=` (617.92) `\text(cm)^2`
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Area of a Triangle Formula
`\text(Area )=1/2 times``\text(base)``times``\text(height)`Area of a Rectangle Formula
`\text(Area )=``\text(length)``times``\text(height)`Showing and Labelling the Surfaces
We need to add the areas of all the faces of the figure: the two triangles and the three rectanglesFirst, to find the area of the triangle, get the height that is perpendicular to its base.Label the sides of the right triangle formed within a triangleUse the Pythagorean Theorem Formula to solve for `a`, which is equal to the `\text(height)``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `\text(h)^2``+``4^2` `=` `7^2` Plug in the known lengths `\text(h)^2+16` `=` `49` Evaluate `4^2` and `7^2` `\text(h)^2` `=` `33` Subtract `16` from both sides `\text(height)` `=` `5.74 \text(cm)` Take the square root of both sides Next, solve for the area of the triangles using the Area of a Triangle formulaNote that there are two triangles with the same lengths, so we will multiply this area by `2` for the surface area`\text(Area)`_{`\text(triangles)`} `=` `1/2 times``\text(base)``times``\text(height)` `=` `1/2 times``8``times``5.74``=``22.96 \text(cm)^2` Now, solve for the area of the rectangles using the Area of a Rectangle formulaNote that there are two rectangles with the same lengths, so we will multiply the first area by `2` for the surface area`\text(Area)`_{`\text(equal rectangles)`} `=` `\text(length)``times``\text(height)` `=` `7``times``26``=``182 \text(cm)^2` `\text(Area)`_{`\text(middle rectangle)`} `=` `\text(length)``times``\text(height)` `=` `8``times``26``=``208 \text(cm)^2` Finally, add all the areas to find the surface area of the figure`\text(SA)` `=` `(2times``22.96``)+(2times``182``)+``208` Plug in the areas `\text(SA)` `=` `617.92 \text(cm)^2` The given measurements are in centimetres, so the area is measured as square centimetres`\text(SA)=617.92 \text(cm)^2` 
Question 2 of 7
2. Question
What is the surface area of this Rectangular Prism?
 Surface Area`=` (320)`mm^2`
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Surface Area of a Rectangular Prism
`SA= 2 xx (color(royalblue)(text(width)) xx color(green)(text(height)) + color(orange)(text(depth)) xx color(green)(text(height)) + color(royalblue)(text(width)) xx color(orange)(text(depth)))`Labelling the given lengths
`color(royalblue)(text(width)=12)``color(green)(text(height)=7)``color(orange)(text(depth)=4)`Use the formula to find the surface area`SA` `=` `2 xx (color(royalblue)(text(width)) xx color(green)(text(height)) + color(orange)(text(depth)) xx color(green)(text(height)) + color(royalblue)(text(width)) xx color(orange)(text(depth)))` Surface area of a Rectangular Prism formula `=` `2 xx (color(royalblue)(text(12)) xx color(green)(text(7)) + color(orange)(text(4)) xx color(green)(text(7)) + color(royalblue)(text(12)) xx color(orange)(text(4)))` Plug in the known lengths `=` `320` Simplify `=` `320 \ mm^2` The given measurements are in millimetres, so the surface area is measured as millimetres squaredVolume`=320 \ mm^2` 
Question 3 of 7
3. Question
Find the surface area of the ConeRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Surface Area )=` (7710.7, 7706.8, 7713.8) `\text(cm)^2`
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Surface Area of a Closed Cone
`\text(SA )=pi times``\text(radius)^2` `+pi times``\text(radius)``times``\text(length)`We need to used the slanted length of the coneShowing and Labelling the Surfaces
We need to add the areas of all the faces of the cone: the curved face and the circular baseFirst, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``52` `\text(radius)` `=` `26` Now, use can use the formula to find the surface area of the closed coneUse `pi=3.141592654` See `pi` explained`\text(SA)` `=` `pi times``\text(radius)^2` `+pi times``\text(radius)``times``\text(length)` Surface Area formula `\text(SA)` `=` `pi times``26^2` `+pi times``26``times``68.4` Plug in the known lengths `\text(SA)` `=` `7710.725` `\text(SA)` `=` `7710.7 \text(cm)^2` Rounded to one decimal place The given measurements are in centimetres, so the area is measured as square centimetres`\text(SA)=7710.7 \text(cm)^2`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `pi=3.141592654` `7710.7 cm^2` `pi=3.14` `7706.8 cm^2` `pi=(22)/(7)` `7713.8 cm^2` 
Question 4 of 7
4. Question
What is the surface area of this cone?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (653.1)`m^2`
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Surface Area of a Cone
`SA=pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))`Labelling the given lengths
`color(darkviolet)(\text(length)=18)``color(royalblue)(\text(radius)=8)`Use the formula to find the surface area`pi~~3.14``SA` `=` `pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))` Surface area of a cone formula `=` `3.14 xx color(royalblue)(8)^2+3.14 xx color(royalblue)(8) xx color(darkviolet)(18)` Plug in the known lengths `=` `3.14 xx 64+3.14 xx 8 xx 18` Simplify `=` `200.96 + 452.16` `=` `653.1 \ m^2` Rounded to 1 decimal place The given measurements are in metres, so the surface area is measured as metres squaredSurface Area`=653.1 \ m^2` 
Question 5 of 7
5. Question
What is the surface area of this cone?
Use `pi~~3.14` Surface Area`=` (785)`mm^2`
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Surface Area of a Cone
`SA=pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))`Labelling the given lengths
`color(darkviolet)(\text(length)=15)``color(forestgreen)(\text(diameter)=20)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(20)` `color(royalblue)(text(radius))` `=` `color(royalblue)(10)` Use the formula to find the surface area`pi~~3.14``SA` `=` `pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))` Surface area of a cone formula `=` `3.14 xx color(royalblue)(10)^2+3.14 xx color(royalblue)(10) xx color(darkviolet)(15)` Plug in the known lengths `=` `3.14 xx 100+3.14 xx 10 xx 15` Simplify `=` `314+471` `=` `785 \ mm^2` The given measurements are in millimetres, so the surface area is measured as millimetres squaredSurface Area`=785 \ mm^2` 
Question 6 of 7
6. Question
Find the surface area of the SphereRound your answer to `1` decimal placeUse `pi=3.141592654` `\text(Surface Area )=` (1520.5, 1519.8, 1521.1) `\text(cm)^2`
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Surface Area of a Sphere
`\text(SA )=4 times pi times``\text(radius)^2`Showing and Labelling the Surfaces
First, recall that the radius is equal to half of the diameter`\text(radius)` `=` `1/2 times ``22` `\text(radius)` `=` `11` Now, you can use the formula to find the surface area of the sphereUse `pi=3.141592654` See `pi` explained`\text(SA)` `=` `4 times pi times``\text(radius)^2` Surface Area formula `\text(SA)` `=` `4 times pi times``11^2` Plug in the known lengths `\text(SA)` `=` `1520.53084` `\text(SA)` `=` `1520.5 \text(cm)^2` Rounded to one decimal place The given measurements are in centimetres, so the area is measured as square centimetres`\text(SA)=1520.5 \text(cm)^2`The answer will depend on which `pi` you use.In this solution we used: `pi=3.141592654`.Using Answer `pi=3.141592654` `1520.5 cm^2` `pi=3.14` `1519.8 cm^2` `pi=(22)/(7)` `1521.1 cm^2` 
Question 7 of 7
7. Question
What is the surface area of this sphere?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (615.4)`cm^2`
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Surface Area of a Sphere
`SA=4 xx pi xx color(royalblue)(text(radius))^2`Labelling the given lengths
`color(forestgreen)(\text(diameter)=14)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(14)` `color(royalblue)(text(radius))` `=` `color(royalblue)(7)` Use the formula to find the surface area`pi~~3.14``SA` `=` `4 xx pi xx color(royalblue)(text(radius))^2` Surface area of a sphere formula `=` `4 xx 3.14 xx color(royalblue)(7)^2` Plug in the known lengths `=` `4 xx 3.14 xx 49` Simplify `=` `615.44` `=` `615.4 \ cm^2` Rounded to 1 decimal place The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=615.4 \ cm^2`
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