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

$2$ decimal places

Use

π \approx 3.14

$pi~~3.14$

Volume $=$ $=$ (718.01) $m^{3}$ $m^3$

Correct

Keep Going!

Incorrect

Volume of a Hemisphere

V = \frac{2}{3} \times π \times {radius}^{3}

$V=2/3 xx pi xx color(royalblue)(\text(radius)^3)$

Labelling the given lengths

radius = 7

$color(royalblue)(\text(radius)=7)$

Use the formula to find the volume

π \approx 3.14

$pi~~3.14$

$V$ $V$	$=$ $=$	$\frac{2}{3} \times π \times {radius}^{3}$ $2/3 xx pi xx color(royalblue)(\text(radius)^3)$	Volume of a hemisphere formula

	$=$ $=$	$\frac{2}{3} \times 3.14 \times 7^{3}$ $2/3 xx 3.14 xx color(royalblue)(7^3)$	Plug in the known lengths

	$=$ $=$	$\frac{2}{3} \times 3.14 \times 343$ $2/3 xx 3.14 xx 343$	Simplify

	$=$ $=$	$718.01 m^{3}$ $718.01 \ m^3$	Rounded to 2 decimal places

The given measurements are in metres, so the volume is measured as metres cubed

Volume

= 718.01 m^{3}

$=718.01 \ m^3$

Question 2 of 7

2. Question

What is the surface area of this cone?

Round your answer to

1

$1$ decimal place

Use

π \approx 3.14

$pi~~3.14$

Surface Area $=$ $=$ (392.5) $c m^{2}$ $cm^2$

Correct

Keep Going!

Incorrect

Surface Area of a Cone

S A = π \times {radius}^{2} + π \times radius \times length

$SA=pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))$

Labelling the given lengths

length = 20

$color(darkviolet)(\text(length)=20)$

radius = 5

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

Use the formula to find the surface area

π \approx 3.14

$pi~~3.14$

$S A$ $SA$	$=$ $=$	$π \times {radius}^{2} + π \times radius \times length$ $pi xx color(royalblue)(text(radius))^2+pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(length))$	Surface area of a cone formula

	$=$ $=$	$3.14 \times 5^{2} + 3.14 \times 5 \times 20$ $3.14 xx color(royalblue)(5)^2+3.14 xx color(royalblue)(5) xx color(darkviolet)(20)$	Plug in the known lengths

	$=$ $=$	$3.14 \times 25 + 3.14 \times 5 \times 20$ $3.14 xx 25+3.14 xx 5 xx 20$	Simplify
	$=$ $=$	$78.5 + 314$ $78.5+314$
	$=$ $=$	$392.5 c m^{2}$ $392.5 \ cm^2$	Rounded to 1 decimal place

The given measurements are in centimetres, so the surface area is measured as centimetres squared

Surface Area

= 392.5 c m^{2}

$=392.5 \ cm^2$

Question 3 of 7

3. Question

What is the volume of this Triangular Prism?

Volume $=$ $=$ (308) $m m^{3}$ $mm^3$

Correct

Keep Going!

Incorrect

Volume of a Triangular Prism

V = \frac{1}{2} \times base \times height \times depth

$V=1/2 xx color(darkviolet)(\text(base)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))$

Labelling the given lengths

base = 8

$color(darkviolet)(\text(base)=8)$

height = 7

$color(royalblue)(\text(height)=7)$

depth = 11

$color(green)(\text(depth)=11)$

Use the formula to find the volume

$V$ $V$	$=$ $=$	$\frac{1}{2} \times width \times height \times depth$ $1/2 xx color(darkviolet)(\text(width)) xx color(royalblue)(\text(height)) xx color(green)(\text(depth))$	Volume of a Triangular Prism formula

	$=$ $=$	$\frac{1}{2} \times 8 \times 7 \times 11$ $1/2 xx color(darkviolet)(\text(8)) xx color(royalblue)(\text(7)) xx color(green)(\text(11))$	Plug in the known lengths

	$=$ $=$	$308$ $308$
	$=$ $=$	$308 m m^{3}$ $308 \ mm^3$

The given measurements are in millimetres, so the volume is measured as millimetres cubed

Volume

= 308 m m^{3}

$=308 \ mm^3$

Question 4 of 7

4. Question

What is the volume of this cone?

Round your answer to

2

$2$ decimal places

Use

π \approx 3.14

$pi~~3.14$

Volume $=$ $=$ (1271.70) $m^{3}$ $m^3$

Correct

Keep Going!

Incorrect

Volume of a Cone

V = \frac{1}{3} \times π \times {radius}^{2} \times height

$V=1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))$

Labelling the given lengths

height = 15

$color(darkviolet)(\text(height)=15)$

radius = 9

$color(royalblue)(\text(radius)=9)$

Use the formula to find the volume

π \approx 3.14

$pi~~3.14$

$V$ $V$	$=$ $=$	$\frac{1}{3} \times π \times {radius}^{2} \times height$ $1/3 xx pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))$	Volume of a cone formula

	$=$ $=$	$\frac{1}{3} \times 3.14 \times 9^{2} \times 15$ $1/3 xx 3.14 xx color(royalblue)(9^2) xx color(darkviolet)(15)$	Plug in the known lengths

	$=$ $=$	$\frac{1}{3} \times 3.14 \times 81 \times 15$ $1/3 xx 3.14 xx 81 xx 15$	Simplify

	$=$ $=$	$1271.70 m^{3}$ $1271.70 \ m^3$	Rounded to 2 decimal places

The given measurements are in metres, so the volume is measured as metres cubed

Volume

= 1271.70 m^{3}

$=1271.70 \ m^3$

Question 5 of 7

5. Question

What is the surface area of this cylinder?

Use

π \approx 3.14

$pi~~3.14$

Surface Area $=$ $=$ (471) $m^{2}$ $m^2$

Correct

Keep Going!

Incorrect

Surface Area of a Cylinder

S A = 2 \times π \times {radius}^{2} + 2 \times π \times radius \times height

$SA=2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$

Labelling the given lengths

height = 10

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

radius = 5

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

Use the formula to find the surface area

π \approx 3.14

$pi~~3.14$

$S A$ $SA$	$=$ $=$	$2 \times π \times {radius}^{2} + 2 \times π \times radius \times height$ $2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$	Surface area of a cylinder formula

	$=$ $=$	$2 \times π \times 5^{2} + 2 \times π \times 5 \times 10$ $2 xx pi xx color(royalblue)(text(5))^2+2 xx pi xx color(royalblue)(\text(5)) xx color(darkviolet)(\text(10))$	Plug in the known lengths

	$=$ $=$	$2 \times 3.14 \times 25 + 2 \times 3.14 \times 5 \times 10$ $2 xx 3.14 xx 25+2 xx 3.14 xx 5 xx 10$	Simplify
	$=$ $=$	$157 + 314$ $157+314$
	$=$ $=$	$471 m^{2}$ $471 \ m^2$	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}

$=471 \ m^2$

Question 6 of 7

6. Question

What is the volume of this Rectangular Prism?

Volume $=$ $=$ (784) $m^{3}$ $m^3$

Correct

Keep Going!

Incorrect

Volume of a Rectangular Prism

V = height \times width \times depth

$V=color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))$

Labelling the given lengths

height = 14

$color(royalblue)(\text(height)=14)$

width = 8

$color(darkviolet)(\text(width)=8)$

depth = 7

$color(green)(\text(depth)=7)$

Use the formula to find the volume

$V$ $V$	$=$ $=$	$height \times width \times depth$ $color(royalblue)(\text(height)) xx color(darkviolet)(\text(width))xx color(green)(\text(depth))$	Volume of a Rectangular Prism formula

	$=$ $=$	$14 \times 8 \times 7$ $color(royalblue)(\text(14)) xx color(darkviolet)(\text(8))xx color(green)(\text(7))$	Plug in the known lengths

	$=$ $=$	$784$ $784$
	$=$ $=$	$784 m^{3}$ $784 \ m^3$

The given measurements are in metres, so the volume is measured as metres cubed

Volume

= 784 m^{3}

$=784 \ m^3$

Question 7 of 7

7. Question

What is the surface area of this cylinder?

Round your answer to

2

$2$ decimal places

Use

π \approx 3.14

$pi~~3.14$

Surface Area $=$ $=$ (678.24) $c m^{2}$ $cm^2$

Correct

Keep Going!

Incorrect

Surface Area of a Cylinder

S A = 2 \times π \times {radius}^{2} + 2 \times π \times radius \times height

$SA= 2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$

Labelling the given lengths

height = 23

$color(darkviolet)(\text(height)=23)$

diameter = 8

$color(forestgreen)(\text(diameter)=8)$

First, recall that the radius is equal to half the diameter

$radius$ $color(royalblue)(text(radius))$	$=$ $=$	$\frac{1}{2} \times 8$ $1/2 xx color(forestgreen)(8)$

$radius$ $color(royalblue)(text(radius))$	$=$ $=$	$4$ $color(royalblue)(4)$

Use the formula to find the surface area

π \approx 3.14

$pi~~3.14$

$S A$ $SA$	$=$ $=$	$2 \times π \times {radius}^{2} + 2 \times π \times radius \times height$ $2 xx pi xx color(royalblue)(text(radius))^2+2 xx pi xx color(royalblue)(\text(radius)) xx color(darkviolet)(\text(height))$	Surface area of a cylinder formula

	$=$ $=$	$2 \times 3.14 \times 4^{2} + 2 \times 3.14 \times 4 \times 23$ $2 xx 3.14 xx color(royalblue)(4)^2+2 xx 3.14 xx color(royalblue)(4) xx color(darkviolet)(23)$	Plug in the known lengths

	$=$ $=$	$2 \times 3.14 \times 16 + 2 \times 3.14 \times 4 \times 23$ $2 xx 3.14 xx 16+2 xx 3.14 xx 4 xx 23$	Simplify
	$=$ $=$	$100.48 + 577.76$ $100.48+577.76$
	$=$ $=$	$678.24 c m^{2}$ $678.24 \ cm^2$	Rounded to 2 decimal places

The given measurements are in centimetres, so the surface area is measured as centimetres squared

Surface Area

= 678.24 c m^{2}

$=678.24 \ cm^2$

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