Surface Area of Shapes 3
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Question 1 of 7
1. Question
Find the surface area of the figure `\text(Surface Area )=` (372) `\text(m)^2`
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Area of a Trapezium Formula
`\text(Area)=1/2 times``\text(height)``times (``\text(base)_1``+``\text(base)_2``)`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 trapezoids and the four rectanglesNext, solve for the area of the trapezoids using the Area of a Trapezium formulaNote that there are two trapezoids with the same lengths, so we will multiply this area by `2` for the surface area`\text(Area)`_{`\text(trapezoids)`} `=` `1/2 times``\text(height)``times (``\text(base)_1``+``\text(base)_2``)` `=` `1/2 times``5``times (``10``+``14``)``=``60 \text(m)^2` Now, solve for the area of the rectangles using the Area of a Rectangle formulaNote that there are two rectangles each with the same lengths, so we will multiply the first area by `2` for the surface area`\text(Area)`_{`\text(side rectangles)`} `=` `\text(length)``times``\text(height)` `=` `6``times``7``=``42 \text(m)^2` `\text(Area)`_{`\text(upper rectangle)`} `=` `\text(length)``times``\text(height)` `=` `10``times``7``=``70 \text(m)^2` `\text(Area)`_{`\text(lower rectangle)`} `=` `\text(length)``times``\text(height)` `=` `14``times``7``=``98 \text(m)^2` Finally, add all the areas to find the surface area of the figure`\text(SA)` `=` `(2times``60``)+(2times``42``)+``70``+``98` Plug in the areas `\text(SA)` `=` `372 \text(m)^2` The given measurements are in metres, so the area is measured as square metres`\text(SA)=372 m^2` 
Question 2 of 7
2. Question
Find the surface area of the HemisphereRound your answer to `2` decimal placesUse `pi=3.141592654` `\text(Surface Area )=` (35995.49, 35977.24, 36009.98) `\text(cm)^2`
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Area of a Circle Formula
`\text(Area)=pi times``\text(radius)^2`Surface Area of a Hemisphere
`\text(SA )=1/2 times 4 times pi times``\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 itselfFirst, find the area of the top circular part using the formula for Area of a CircleUse `pi=3.141592654` See `pi` explained`\text(Area)`_{`\text(top part)`} `=` `pi times``\text(radius)^2` `=` `pi times``61.8^2` `=` `11998.49633 \text(cm)^2` Next, use the formula to find the surface area of the hemisphere (half the formula for the Sphere)Use `pi=3.141592654` See `pi` explained`\text(SA)`_{`\text(hemisphere)`} `=` `1/2 times 4 times pi times``\text(radius)^2` `=` `1/2 times 4 times pi times``61.8^2` `=` `23996.99265 \text(cm)^2` Finally, add the areas to find the surface area of the figure`\text(SA)` `=` `11998.49633``+``23996.99265` Plug in the areas `\text(SA)` `=` `35995.49 \text(cm)^2` Rounded to two decimal places The given measurements are in centimetres, so the area is measured as square centimetres`\text(SA)=35995.49 \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` `35995.49 cm^2` `pi=3.14` `35977.24 cm^2` `pi=(22)/(7)` `36009.98 cm^2` 
Question 3 of 7
3. Question
What is the surface area of this sphere?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (452.2)`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(royalblue)(\text(radius)=6)`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)(text(6))^2` Plug in the known lengths `=` `4 xx 3.14 xx 36` Simplify `=` `452.16` `=` `452.2 \ cm^2` Rounded to 1 decimal place The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=452.2 \ cm^2` 
Question 4 of 7
4. Question
What is the surface area of this half sphere?
Round your answer to `2` decimal placesUse `pi~~3.14` Surface Area`=` (3052.08)`mm^2`
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Area of a Circle Formula
`\text(Area)=pi times``\text(radius)^2`Surface Area of a Hemisphere
`\text(SA )=2 times pi times``\text(radius)^2`We need to add the areas of all the faces of the hemisphere: the flat circular part and the hemisphere itselfFirst, find the area of the top circular part using the formula for Area of a Circle`\text(Area)`_{`\text(top part)`} `=` `pi times``\text(radius)^2` `=` `pi times``18^2``=``1,017.36 \text(mm)^2` Next, use the formula to find the surface area of the hemisphere (half the formula for the Sphere)`\text(SA)`_{`\text(hemisphere)`} `=` `1/2 times 4 times pi times``\text(radius)^2` `=` `1/2 times 4 times pi times``18^2``=``2,034.72 \text(mm)^2` Finally, add the areas to find the surface area of the figure`\text(SA)` `=` `1,017.36``+``2,034.72` Plug in the areas `\text(SA)` `=` `3,052.08 \text(mm)^2` Rounded to two decimal places The given measurements are in millimetres, so the area is measured as square millimetres`\text(SA)=3,052.08 \text(mm)^2` 
Question 5 of 7
5. Question
What is the surface area of this sphere?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (1017.4)`m^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)=18)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(18)` `color(royalblue)(text(radius))` `=` `color(royalblue)(9)` 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)(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 The given measurements are in metres, so the surface area is measured as metres squaredSurface Area`=1,017.4 \ m^2` 
Question 6 of 7
6. Question
What is the surface area of this cylinder?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (1758.4)`mm^2`
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Surface Area of a Cylinder
`SA=2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=27)``color(royalblue)(\text(radius)=8)`Use the formula to find the surface area`pi~~3.14``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 The given measurements are in millimetres, so the surface area is measured as millimetres squaredSurface Area`=1,758.4 \ mm^2` 
Question 7 of 7
7. Question
What is the surface area of this cylinder?
Round your answer to `2` decimal placesUse `pi~~3.14` Surface Area`=` (2204.28)`mm^2`
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Surface Area of a Cylinder
`SA=2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=30)``color(royalblue)(\text(radius)=9)`Use the formula to find the surface area`pi~~3.14``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 The given measurements are in millimetres, so the surface area is measured as millimetres squaredSurface Area`=2,204.28 \ mm^2`
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