Mathematics · Geometry

Similar-Solid Volume Scale Calculator

Calculate similar solid volume from original solid volume and linear scale factor.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
similar solid volume699.84

Calculation steps

  1. Use c=ab³ with original solid volume=120 and linear scale factor=1.8.
  2. similar solid volume=699.8400000000001.

Understand Similar-Solid Volume Scale

One idea, three depths

Choose how deeply to explain Similar-Solid Volume Scale

Similar-Solid Volume Scale: Calculate similar solid volume from original solid volume and linear scale factor.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Similar-Solid Volume Scale to answer this question: calculate similar solid volume from original solid volume and linear scale factor? Enter original solid volume and linear scale factor; the calculator shows similar solid volume. For example: original solid volume=120 and linear scale factor=1.8 produce similar solid volume=699.8400000000001. The answer tells you similar solid volume.

Age 15Explain it to a 15-year-oldConnect it to the formula

Volumes of similar solids change with the cube of their corresponding length ratio. This page evaluates the relationship directly. The rule is c=ab³. Its input values are original solid volume, linear scale factor, and the main result is similar solid volume. For example: original solid volume=120 and linear scale factor=1.8 produce similar solid volume=699.8400000000001.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated similar-solid volume scale relation over the valid real-number domain stated below. The implemented relation is c=ab³, evaluated from original solid volume, linear scale factor to produce similar solid volume. Volumes of similar solids change with the cube of their corresponding length ratio. This page evaluates the relationship directly. The formula requires geometrically similar solids, not only equal heights or equal base shapes.

Inputs and valid domain

  • original solid volume must be a finite real number.
  • linear scale factor must be a finite real number.

Important boundary: The formula requires geometrically similar solids, not only equal heights or equal base shapes.

The formula

c=ab³

How the calculator works through it

It substitutes original solid volume, linear scale factor into the formula and exposes every numerical step above. The main output is similar solid volume.

Read the result correctly

The similar solid volume is the direct answer to “calculate similar solid volume from original solid volume and linear scale factor.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

original solid volume=120 and linear scale factor=1.8 produce similar solid volume=699.8400000000001.

Where this model stops being reliable

The formula requires geometrically similar solids, not only equal heights or equal base shapes.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Similar-Solid Volume Scale works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Similar-Solid Volume Scale uses c=ab³. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

  • Angles and geometric relationships

    Angle language provides useful geometric context for extending Similar-Solid Volume Scale to related shapes and constructions.

    Review this foundation about 4 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read original solid volume, linear scale factor.
  2. Evaluate the principal relationship: c=ab³.
  3. Return similar solid volume and check the domain conditions described above.
Python
            from math import *

def similar_solid_volume_scale_calculator(a, b) -> float:
    return (a * pow(b, 3.0))

assert abs(similar_solid_volume_scale_calculator(120, 1.8) - 699.8400000000001) < 1e-6 * max(1.0, abs(699.8400000000001))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double similar_solid_volume_scale_calculator(double a, double b) {
    return (a * pow(b, 3.0));
}

int main(void) {
    const double expected = 699.8400000000001;
    const double actual = similar_solid_volume_scale_calculator(120, 1.8);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double similar_solid_volume_scale_calculator(double a, double b) {
    return (a * std::pow(b, 3.0));
}

int main() {
    constexpr double expected = 699.8400000000001;
    const double actual = similar_solid_volume_scale_calculator(120, 1.8);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double similar_solid_volume_scale_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern pow
global similar_solid_volume_scale_calculator
section .text

similar_solid_volume_scale_calculator:
    push rbp
    mov rbp, rsp
    sub rsp, 48
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    mov rax, 0x4008000000000000
    movq xmm0, rax
    movsd [rbp-40], xmm0
    movsd xmm0, [rbp-16]
    movsd xmm1, [rbp-40]
    call pow wrt ..plt
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-32]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = similar_solid_volume_scale_calculator(a, b)
    result = (a * (b ^ 3.0));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * (b ^ 3.0));
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Similar-Solid Volume Scale Calculator. MW SysArc Tools. https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator

MLA 9

MW SysArc. “Similar-Solid Volume Scale Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Similar-Solid Volume Scale Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator.

Harvard

MW SysArc (2026) ‘Similar-Solid Volume Scale Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_similar_solid_volume_scale_calculator_2026,
  author = {{MW SysArc}},
  title = {Similar-Solid Volume Scale Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Similar-Solid Volume Scale Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/geometry/similar-solid-volume-scale-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Similar-Solid Volume Scale do?

Calculate similar solid volume from original solid volume and linear scale factor.

How does the Similar-Solid Volume Scale work?

The calculator applies c=ab³. Volumes of similar solids change with the cube of their corresponding length ratio. This page evaluates the relationship directly.

What can I learn from the Similar-Solid Volume Scale?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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