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Surface Area and Volume Mixed Review>
Surface Area and Volume Mixed Review 2Surface Area and Volume Mixed Review 2
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Question 1 of 7
1. Question
What is the volume of this hemisphere?
Round your answer to `2` decimal placesUse `pi~~3.14`- Volume`=` (718.01)`m^3`
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Volume of a Hemisphere
`V=2/3 xx pi xx color(royalblue)(\text(radius)^3)`Labelling the given lengths
`color(royalblue)(\text(radius)=7)`Use the formula to find the volume`pi~~3.14``V` `=` `2/3 xx pi xx color(royalblue)(\text(radius)^3)` Volume of a hemisphere formula `=` `2/3 xx 3.14 xx color(royalblue)(7^3)` Plug in the known lengths `=` `2/3 xx 3.14 xx 343` Simplify `=` `718.01 \ m^3` Rounded to 2 decimal places The given measurements are in metres, so the volume is measured as metres cubedVolume`=718.01 \ m^3` -
Question 2 of 7
2. Question
What is the surface area of this cone?
Round your answer to `1` decimal placeUse `pi~~3.14`- Surface Area`=` (392.5)`cm^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)=20)``color(royalblue)(\text(radius)=5)`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)(5)^2+3.14 xx color(royalblue)(5) xx color(darkviolet)(20)` Plug in the known lengths `=` `3.14 xx 25+3.14 xx 5 xx 20` Simplify `=` `78.5+314` `=` `392.5 \ cm^2` Rounded to 1 decimal place The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=392.5 \ cm^2` -
Question 3 of 7
3. Question
What is the volume of this Triangular Prism?
- Volume`=` (308)`mm^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)=8)``color(royalblue)(\text(height)=7)``color(green)(\text(depth)=11)`Use the formula to find the volume`V` `=` `1/2 xx color(darkviolet)(\text(width)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))` Volume of a Triangular Prism formula `=` `1/2 xx color(darkviolet)(\text(8)) xx color(royalblue)(\text(7)) xx color(green)(\text(11))` Plug in the known lengths `=` `308` `=` `308 \ mm^3` The given measurements are in millimetres, so the volume is measured as millimetres cubedVolume`=308 \ mm^3` -
Question 4 of 7
4. Question
What is the volume of this cone?
Round your answer to `2` decimal placesUse `pi~~3.14`- Volume`=` (1271.70)`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)=15)``color(royalblue)(\text(radius)=9)`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)(9^2) xx color(darkviolet)(15)` Plug in the known lengths `=` `1/3 xx 3.14 xx 81 xx 15` Simplify `=` `1271.70 \ m^3` Rounded to 2 decimal places The given measurements are in metres, so the volume is measured as metres cubedVolume`=1271.70 \ m^3` -
Question 5 of 7
5. Question
What is the surface area of this cylinder?
Use `pi~~3.14`- Surface Area`=` (471)`m^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)=10)``color(royalblue)(\text(radius)=5)`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(5))^2+2 xx pi xx color(royalblue)(\text(5)) xx color(darkviolet)(\text(10))` Plug in the known lengths `=` `2 xx 3.14 xx 25+2 xx 3.14 xx 5 xx 10` Simplify `=` `157+314` `=` `471 \ m^2` Rounded to 1 decimal place The given measurements are in metres, so the surface area is measured as metres squaredSurface Area`=471 \ m^2` -
Question 6 of 7
6. Question
What is the volume of this Rectangular Prism?
- Volume`=` (784)`m^3`
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Volume of a Rectangular Prism
`V=color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))`Labelling the given lengths
`color(royalblue)(\text(height)=14)``color(darkviolet)(\text(width)=8)``color(green)(\text(depth)=7)`Use the formula to find the volume`V` `=` `color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))` Volume of a Rectangular Prism formula `=` `color(royalblue)(\text(14)) xx color(darkviolet)(\text(8))xx color(green)(\text(7))` Plug in the known lengths `=` `784` `=` `784 \ m^3` The given measurements are in metres, so the volume is measured as metres cubedVolume`=784 \ m^3` -
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`=` (678.24)`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)=23)``color(forestgreen)(\text(diameter)=8)`First, recall that the radius is equal to half the diameter`color(royalblue)(text(radius))` `=` `1/2 xx color(forestgreen)(8)` `color(royalblue)(text(radius))` `=` `color(royalblue)(4)` 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)(4)^2+2 xx 3.14 xx color(royalblue)(4) xx color(darkviolet)(23)` Plug in the known lengths `=` `2 xx 3.14 xx 16+2 xx 3.14 xx 4 xx 23` Simplify `=` `100.48+577.76` `=` `678.24 \ cm^2` Rounded to 2 decimal places The given measurements are in centimetres, so the surface area is measured as centimetres squaredSurface Area`=678.24 \ 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