Surface 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 places

Use

$pi~~3.14$

Volume $=$ (2712.96) $m^3$

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

$color(darkviolet)(\text(height)=18)$

$color(royalblue)(\text(radius)=12)$

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 cubed

Volume

$=2,712.96 \ m^3$

Question 2 of 7

2. Question

What is the surface area of this sphere?

Round your answer to

$1$ decimal place

Use

$pi~~3.14$

Surface Area $=$ (1519.8) $mm^2$

Correct

Keep Going!

Incorrect

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 squared

Surface Area

$=1,519.8 \ mm^2$

Question 3 of 7

3. Question

What is the volume of this Triangular Prism?

Volume $=$ (351) $cm^3$

Correct

Keep Going!

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

$color(darkviolet)(\text(base)=9)$

$color(royalblue)(\text(height)=6)$

$color(green)(\text(depth)=13)$

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 cubed

Volume

$=351 \ cm^3$

Question 4 of 7

4. Question

What is the surface area of this cylinder?

Round your answer to

$1$ decimal place

Use

$pi~~3.14$

Surface Area $=$ (1758.4) $mm^2$

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

$color(darkviolet)(\text(height)=27)$

$color(royalblue)(\text(radius)=8)$

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 squared

Surface 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 places

Use

$pi~~3.14$

Volume $=$ (3818.24) $cm^3$

Correct

Keep Going!

Incorrect

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 cubed

Volume

$=3,818.24 \ cm^3$

Question 6 of 7

6. Question

What is the surface area of this cylinder?

Use

$pi~~3.14$

Surface Area $=$ (471) $cm^2$

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

$color(darkviolet)(\text(height)=22)$

$color(royalblue)(\text(radius)=3)$

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 squared

Surface Area

$=471 \ cm^2$

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 $=$ (2003.32) $cm^2$

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

$color(darkviolet)(\text(height)=18)$

$color(forestgreen)(\text(diameter)=22)$

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 squared

Surface 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