Surface 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 places

Use `pi~~3.14`

Volume`=` (718.01)`m^3`

Correct

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Incorrect

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 cubed

Volume`=718.01 \ m^3`

Question 2 of 7

2. Question

What is the surface area of this cone?

Round your answer to `1` decimal place

Use `pi~~3.14`

Surface Area`=` (392.5)`cm^2`

Correct

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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 squared

Surface Area`=392.5 \ cm^2`

Question 3 of 7

3. Question

What is the volume of this Triangular Prism?

Volume`=` (308)`mm^3`

Correct

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Incorrect

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 cubed

Volume`=308 \ mm^3`

Question 4 of 7

4. Question

What is the volume of this cone?

Round your answer to `2` decimal places

Use `pi~~3.14`

Volume`=` (1271.70)`m^3`

Correct

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Incorrect

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 cubed

Volume`=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`

Correct

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Incorrect

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 squared

Surface Area`=471 \ m^2`

Question 6 of 7

6. Question

What is the volume of this Rectangular Prism?

Volume`=` (784)`m^3`

Correct

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Incorrect

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 cubed

Volume`=784 \ m^3`

Question 7 of 7

7. Question

What is the surface area of this cylinder?

Round your answer to `2` decimal places

Use `pi~~3.14`

Surface Area`=` (678.24)`cm^2`

Correct

Keep Going!

Incorrect

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 squared

Surface 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