Mathematical formulae - Volume - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Aiden McCall	said	Needs to be tested	7 years, 9 months ago
Lauren Richards	said	Has some problems	7 years, 9 months ago

History

○

Elliott Fletcher 7 years, 8 months ago

Published this.

○

Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

○

Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Looks OK.

Restore this checkpoint

○

Aiden McCall 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Lauren Richards 7 years, 9 months ago

Gave some feedback: Has some problems

○

Lauren Richards commented 7 years, 9 months ago

You could put the equations for calculating volume for the individual shapes in the actual question or at the start of the advice or as a (show steps) stage.

You could state what each shape is, or have an introductory statement for each part instead of the overall question statement that generalises all the shapes like "Calculate the volume of the following rectangular-based pyramid.".

The little shapes next to Area are awesome. The colourful diagrams are also mint.

Make sure you have a full stop after all the final answers in the advice section and you're missing one at the end of the second bit of text in part b) (advice) after depth = []m. This is also true for the second text part of part c) and d).

The answer in the advice for part d) is not the same as the expected answer in the question. The advice is the one that is incorrect. You have used h instead of 1/3(h) in the second part.

Great question! :)

○

Aiden McCall 7 years, 9 months ago

Gave some feedback: Needs to be tested

○

Aiden McCall 7 years, 9 months ago

Created this.

Name	Status	Author	Last Modified
Mathematical formulae - Volume	Ready to use	Aiden McCall	19/12/2022 12:22
Johan's copy of Mathematical formulae - Volume berekeningen	draft	Johan Maertens	21/08/2017 20:29
Johan's copy of Mathematical formulae - Volume	draft	Johan Maertens	21/08/2017 20:29
Kwame's copy of Mathematical formulae - Volume	draft	Kwame D Dwamena	15/06/2019 14:51
GA4 Volume of a triangular prism	Ready to use	Megan Oliver	09/04/2024 17:45
GA5 Volume of cylinder	Ready to use	Megan Oliver	09/04/2024 17:46

There are 5 other versions that do you not have access to.

Question statement

Calculate the volumes of the following shapes.

Give any introductory information the student needs.

			Name	Type	Generated Value

w4	number	7.1
d4	integer	3
h4	integer	4

			Name	Type	Generated Value

w6	integer	8
h6	integer	2
d6	number	11.5

			Name	Type	Generated Value

			r7	integer	3
			w7	number	11.2

			Name	Type	Generated Value

h8	integer	7
w8	integer	6
d8	number	5.8

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5.5..8#0.1)

JME function reference

Description

Width of cuboid.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

7.1

→ Used by:

Advice
"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part c) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part d) Gap-fill
1. Gap Number entry
  Add
1. Step Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Calculate the $\mathrm{Volume}$ of the following cuboid.

$\mathrm{Volume} =$ Unnamed gap $\mathrm{m}^3$ .

Advice

For a cuboid, we first need to find out the area of one of the faces then multiply this area by the depth of the object.
In this example you can choose either of the faces. To make the calculations easier I am going to choose the face with $\mathrm{base} = \var{d4}m$ and $\mathrm{height}= \var{h4}m\thinspace$ .

$\begin{align} \mathrm{Area\thinspace_\square} &= \mathrm{base} \times \mathrm{height} \\ &= \var{h4} \times \var{d4} \\ &= \var{h4*d4}\, \mathrm{m}^2\,. \end{align}$

Now that we have the area of the face ( $\mathrm{Area\thinspace_\square}$ ) we can multiply this by the $\mathrm{depth} = \var{w4}m$ to calculate the volume of the object.

$\begin{align} \mathrm{Volume} &= \mathrm{Area\thinspace_\square} \times \mathrm{depth} \\ &= \var{h4*d4} \times \var{w4} \\ &= \var{h4*d4*w4}\, \mathrm{m}^3\,. \end{align}$

For a triangular prism, we first need to find the area of one of the faces then multiply this area by the depth of the prism.
In this example the easiest way to calculate the volume is to take the area of the triangular face first with $\mathrm{base} = \var{w6}m$ and $\mathrm{height} = \var{h6}m\thinspace$ .

$\begin{align} \mathrm{Area\thinspace_\triangle} &= \frac{\mathrm{base} \times \mathrm{height}}{2} \\ &= \frac{\var{w6} \times \var{h6}}{2} \\ &= \var{0.5*w6*h6}\, \mathrm{m}^2\,. \end{align}$

Now that we have the area of the triangular face ( $\mathrm{Area\thinspace_\triangle}$ ) we can multiply this by the $\mathrm{depth} = \var{d6}m\thinspace$ .

$\begin{align} \mathrm{Volume} &= \mathrm{Area\thinspace_\triangle} \times \mathrm{depth} \\ &= \var{w6*h6} \times \var{d6} \\ &= \var{w6*h6*d6}\, \mathrm{m}^2\,. \end{align}$

For a cylinder, we first need to find the area of the circular face then multiply this area by the depth of the cylinder.
In this example the radius of the circular face is $\mathrm{radius} = \var{r7}m$ which can be used to calculate the area of the circular face.

$\begin{align} \mathrm{Area\thinspace_\bigcirc} &= \pi \times \mathrm{radius}^2 \\ &= \pi \times \var{r7}^2 \\ &= \var{pi * (r7)^2}\, \mathrm{m}^2 \,. \end{align}$

Now that we have the area of the circular face ( $\mathrm{Area\thinspace_\bigcirc}$ ) we can multiply this by the $\mathrm{depth} =\var{w7}m\thinspace$ .

$\begin{align} \mathrm{Volume} &= \mathrm{Area\thinspace_\bigcirc} \times \mathrm{depth} \\ &= \var{pi*(r7)^2} \times \var{w7} \\ &= \var{dpformat(pi*w7*(r7)^2, 5)} \\ &= \var{dpformat(pi*w7*(r7)^2, 1)}\, \mathrm{m}^2\,. \quad \text{1 d.p.} \end{align}$

d)
For a rectangular-based pyramid, we first need to calculate the area of the base and multiply this area by $\frac{1}{3}$ the height of the pyramid.
In this example the area of the base can be calculated from the $\mathrm{width}= \var{w8}m$ and $\mathrm{length} = \var{d8}m\thinspace$ .

$\begin{align} \mathrm{Area\thinspace_\boxdot} &= \mathrm{width} \times \mathrm{length} \\ &= \var{w8} \times \var{d8} \\ &= \var{w8*d8}\, \mathrm{m}^2\,. \end{align}$

Now that we have the area of the base we can multiply this by the $\frac{1}{3} \mathrm{height}$ where $\mathrm{height} = \var{h8}m\thinspace$ .

$\begin{align} \mathrm{Volume} &= \mathrm{Area\thinspace_\boxdot} \times \frac{1}{3} \mathrm{height} \\ &= \var{w8*d8} \times \var{dpformat(1/3*h8,5)}\\ &= \var{dpformat(w8*d8*h8*1/3,5)}\\ &= \var{dpformat(w8*d8*h8*1/3,1)}\, \mathrm{m}^3\,. \quad \text{1 d.p.} \end{align}$

Give a worked solution to the whole question.

URL

Text alternative
URL

Text alternative
URL

Text alternative
URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only

This question is used in the following exams:

WBL Level 2 Diagnostic Assessment by john halder in john's workspace.
WBL Level 2 Diagnostic Assessment by john halder in john's workspace.
Module 3 by Niharika Singh in Niharika's workspace.
Transition Formula by Chris Templet in Chris's workspace.
All the good stuff by Chris Templet in Chris's workspace.

Loading...

Error

Mathematical formulae - Volume

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Aiden McCall 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Mathematical formulae - Volume

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Aiden McCall 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Aiden McCall 7 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`