Volume of Shapes 3

Topics

Geometry

Surface Area and Volume

Volume of Shapes

Volume of Shapes 3

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Question 1 of 7

Find the volume of the Hemisphere

Round your answer to

$1$ decimal place

Use

$pi=3.141592654$

$\text(Volume )=$ (41.2) $\text(m)^3$

Using	Answer
$pi=3.141592654$	$41.2 m^3$
$pi=3.14$	$41.2 m^3$
$pi=(22)/(7)$	$41.2 m^3$

Question 2 of 7

What is the volume of this cone?

Round your answer to

$2$ decimal places

Use

$pi~~3.14$

Volume $=$ (287.83) $cm^3$

Question 3 of 7

What is the volume of this sphere?

Round your answer to

$2$ decimal places

Use

$pi~~3.14$

Volume $=$ (113.04) $mm^3$

Question 4 of 7

Find the volume of the Pyramid

$\text(Volume )=$ (1456) $\text(m)^3$

Question 5 of 7

Find the volume of the Cone

Round your answer to the nearest whole number

Use

$pi=3.141592654$

$\text(Volume )=$ (2545, 2543, 2546) $\text(cm)^3$

Using	Answer
$pi=3.141592654$	$2545 cm^3$
$pi=3.14$	$2543 cm^3$
$pi=(22)/(7)$	$2546 cm^3$

Question 6 of 7

What is the volume of this cylinder?

Round your answer to

$2$ decimal places

Use

$pi~~3.14$

Volume $=$ (1808.64) $m^3$

Question 7 of 7

Find the volume of the figure

Round your answer to

$2$ decimal places

Use

$pi=3.141592654$

$\text(Volume )=$ (1449.15, 1448.42, 1449.74) $\text(mm)^3$

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Volume of a Fractional Circle

$\text{Volume}\;=\;\frac{\color{#e85e00}{θ}}{360°}\times π \times \color{#0079a2}{\text{radius}^2} \times \color{#9a00c7}{\text{depth}}$

Labelling the given lengths

$\text(radius)=8$

$theta=279°$

$\text(depth)=9.3$

First, find the area of the front face

Use

$pi=3.141592654$ See

$pi$ explained

$\text(Area)$	$=$	$\frac{\color{#e85e00}{θ}}{360°}\times π \times \color{#0079a2}{\text{radius}^2}$	Area of a Fractional Circle

	$=$	$\frac{\color{#e85e00}{279°}}{360°}\times π \times \color{#0079a2}{8^2}$	Plug in the known lengths

	$=$	$0.775 \times 3.141592654 \times \color{#0079a2}{8^2}$	Plug in the known lengths
	$=$	$155.82299 \text(mm)^2$

Next, multiply the area by the depth to find the volume

$\text(Volume)$	$=$	$\text(area)$ $times$ $\text(depth)$	Finding the volume
	$=$	$155.82299$ $times$ $9.3$	Plug in the known lengths
	$=$	$1449.153807$
	$=$	$1449.15 \text(mm)^3$	Round to $2$ decimal places

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

$\text(Volume)=1449.15 \text(mm)^3$

The answer will depend on which

$pi$ you use.

In this solution we used:

$pi=3.141592654$ .

Using	Answer
$pi=3.141592654$	$1449.15 mm^3$
$pi=3.14$	$1448.42 mm^3$
$pi=(22)/(7)$	$1449.74 mm^3$

$\text(Volume)$	$=$	$1/2 times 4/3 times pi times$ $\text(radius)^3$	Volume of a Hemisphere formula

	$=$	$1/2 times 4/3 times 3.141592654 times$ $2.7^3$	Plug in the known lengths

	$=$	$1/2 times 4/3 times 3.141592654 times 19.683$	Simplify

	$=$	$41.22397$
	$=$	$41.2 \text(m)^3$	Rounded to $1$ decimal place

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

	$=$	$1/3 xx 3.14 xx color(royalblue)(5^2) xx color(darkviolet)(11)$	Plug in the known lengths

	$=$	$1/3 xx 3.14 xx 25 xx 11$	Simplify

	$=$	$287.83333$
	$=$	$287.83 \ cm^3$	Rounded to 2 decimal places

$V$	$=$	$4/3 xx pi xx color(royalblue)(\text(radius)^3)$	Volume of a sphere formula

	$=$	$4/3 xx 3.14 xx color(royalblue)(3^3)$	Plug in the known lengths

	$=$	$4/3 xx 3.14 xx 27$	Simplify

	$=$	$113.04 \ mm^3$	Rounded to 2 decimal places

$\text(Volume)$	$=$	$1/3 times pi times$ $\text(radius)^2$ $times$ $\text(height)$	Volume of a Cone formula

	$=$	$1/3 times 3.141592654 times$ $9^2$ $times$ $30$	Plug in the known lengths

	$=$	$1/3 times 3.141592654 times 81 times 30$	Simplify

	$=$	$2544.69$
	$=$	$2545 \text(cm)^3$	Rounded to the nearest whole number

$V$	$=$	$pi xx color(royalblue)(\text(radius)^2) xx color(darkviolet)(\text(height))$	Volume of a cylinder formula

	$=$	$3.14 xx color(royalblue)(8^2) xx color(darkviolet)(13)$	Plug in the known lengths

	$=$	$3.14 xx 64 xx 9$	Simplify

	$=$	$1,808.64 \ m^3$	Rounded to 2 decimal places

Volume of Shapes 3

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Quiz summary

Information

1. Question

Hint

Excellent!

Volume of a Hemisphere

Labelling the given lengths

2. Question

Keep Going!

Volume of a Cone

Labelling the given lengths

3. Question

Keep Going!

Volume of a Cone

Labelling the given lengths

4. Question

Hint

Keep Going!

Volume of a Pyramid

Labelling the given lengths

5. Question

Hint

Correct!

Volume of a Cone

Labelling the given lengths

6. Question

Keep Going!

Volume of a Cylinder

Labelling the given lengths

7. Question

Hint

Correct!

Volume of a Fractional Circle

Labelling the given lengths

Quizzes

$\text(Area)$	$=$	$\text(length)$ $times$ $\text(width)$	Area of a Rectangle
	$=$	$21$ $times$ $8$	Plug in the known lengths
	$=$	$168 \text(m)^2$

$\text(Volume)$	$=$	$1/3 times$ $\text(length)$ $times$ $\text(width)$ $times$ $\text(height)$	Volume of a Pyramid
	$=$	$1/3 times$ $168$ $times$ $26$	Plug in the known lengths
	$=$	$1456 \text(m)^3$