Mathematics · Geometry
Similar-Solid Volume Scale Calculator
Calculate similar solid volume from original solid volume and linear scale factor.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ab³ with original solid volume=120 and linear scale factor=1.8.
- 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
- Ratios between measured quantities
Ratios help you check the scale, units and proportional meaning of Similar-Solid Volume Scale.
Review this foundation about 4 min
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
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
- Read original solid volume, linear scale factor.
- Evaluate the principal relationship: c=ab³.
- 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))
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)));
}
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)));
}
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
MATLAB
function result = similar_solid_volume_scale_calculator(a, b)
result = (a * (b ^ 3.0));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * (b ^ 3.0));
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 chaptersCite 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 .