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Surface Area and Volume Mixed Review>
Surface Area and Volume Mixed Review 3Surface Area and Volume Mixed Review 3
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Question 1 of 7
1. Question
What is the volume of this cone?
Round your answer to `2` decimal placesUse `pi~~3.14` Volume`=` (2712.96)`m^3`
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Volume of a Cone
`V=1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=18)``color(royalblue)(\text(radius)=12)`Use the formula to find the volume`pi~~3.14``V` `=` `1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))` Volume of a cone formula `=` `1/3 xx 3.14 xx color(royalblue)(12^2) xx color(darkviolet)(18)` Plug in the known lengths `=` `1/3 xx 3.14 xx 144 xx 18` Simplify `=` `2,712.96 \ m^3` Rounded to 2 decimal places The given measurements are in metres, so the volume is measured as metres cubedVolume`=2,712.96 \ m^3` 
Question 2 of 7
2. Question
What is the surface area of this sphere?
Round your answer to `1` decimal placeUse `pi~~3.14` Surface Area`=` (1519.8)`mm^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)=22)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(22)` `color(royalblue)(text(radius))` `=` `color(royalblue)(11)` 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(11))^2` Plug in the known lengths `=` `4 xx 3.14 xx 121` Simplify `=` `1,519.76` `=` `1,519.8 \ mm^2` Rounded to 1 decimal place The given measurements are in millimetres, so the surface area is measured as millimetres squaredSurface Area`=1,519.8 \ mm^2` 
Question 3 of 7
3. Question
What is the volume of this Triangular Prism?
 Volume`=` (351)`cm^3`
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Volume of a Triangular Prism
`V=1/2 xx color(darkviolet)(\text(base)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))`Labelling the given lengths
`color(darkviolet)(\text(base)=9)``color(royalblue)(\text(height)=6)``color(green)(\text(depth)=13)`Use the formula to find the volume`V` `=` `1/2 xx color(darkviolet)(\text(base)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))` Volume of a Triangular Prism formula `=` `1/2 xx color(darkviolet)(\text(9)) xx color(royalblue)(\text(6)) xx color(green)(\text(13))` Plug in the known lengths `=` `351` `=` `351 \ cm^3` The given measurements are in centimetres, so the volume is measured as centimetres cubedVolume`=351 \ cm^3` 
Question 4 of 7
4. 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 5 of 7
5. Question
What is the volume of this cylinder?
Round your answer to `2` decimal placesUse `pi~~3.14` Volume`=` (3818.24)`cm^3`
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Volume of a Cylinder
`V=pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))`Labelling the given lengths
`color(darkviolet)(\text(height)=19)``color(royalblue)(\text(radius)=8)`Use the formula to find the volume`pi~~3.14``V` `=` `pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))` Volume of a cylinder formula `=` `3.14 xx color(royalblue)(8^2) xx color(darkviolet)(19)` Plug in the known lengths `=` `3.14 xx 64 xx 19` Simplify `=` `3,818.24` `=` `3,818.24 \ cm^3` Rounded to 2 decimal places The given measurements are in centimetres, so the volume is measured as centimetres cubedVolume`=3,818.24 \ cm^3` 
Question 6 of 7
6. Question
What is the surface area of this cylinder?
Use `pi~~3.14` Surface Area`=` (471)`cm^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)=22)``color(royalblue)(\text(radius)=3)`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(3))^2+2 xx pi xx color(royalblue)(\text(3)) xx color(darkviolet)(\text(22))` Plug in the known lengths `=` `2 xx 3.14 xx 9+2 xx 3.14 xx 3 xx 22` Simplify `=` `56.52+414.48` `=` `471 \ cm^2` Rounded to 1 decimal place The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=471 \ cm^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`=` (2003.32)`cm^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)=18)``color(forestgreen)(\text(diameter)=22)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(22)` `color(royalblue)(text(radius))` `=` `color(royalblue)(11)` 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 3.14 xx color(royalblue)(11)^2+2 xx 3.14 xx color(royalblue)(11) xx color(darkviolet)(18)` Plug in the known lengths `=` `2 xx 3.14 xx 121+2 xx 3.14 xx 11 xx 18` Simplify `=` `759.88+1243.44` `=` `2,003.32 \ cm^2` Rounded to 2 decimal places The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=2,003.32 \ cm^2`
Quizzes
 Volume of Shapes 1
 Volume of Shapes 2
 Volume of Shapes 3
 Volume of Shapes 4
 Volume of Composite Shapes 1
 Volume of Composite Shapes 2
 Surface Area of Shapes 1
 Surface Area of Shapes 2
 Surface Area of Shapes 3
 Surface Area and Volume Mixed Review 1
 Surface Area and Volume Mixed Review 2
 Surface Area and Volume Mixed Review 3
 Surface Area and Volume Mixed Review 4