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

Keep Going!

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

Keep Going!

Incorrect

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

Keep Going!

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

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

$color(darkviolet)(\text(height)=10)$

$color(royalblue)(\text(radius)=5)$

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

Keep Going!

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