DuckieDai Frustum Volume Python Program

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geometry · MIT License

Overview

Solve frustum volume, height, or either base area using the square-root frustum-volume formula.

Usage

Inputs

Requested unknown: volume, height, or one base area
Three known positive values

Outputs

Requested frustum quantity with formula and units

Units: Height uses length units, base areas use squared units, and volume uses cubed units.

Assumptions and limitations

Assumptions

A1 and A2 are positive parallel base areas of one frustum.

Constraints

All entered values must be positive and below 1e100.

Known failures

Inconsistent units produce an incorrect result.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact source owner-tested through TI Connect CE
What happened: Owner confirmed the supplied frustum volume program runs on the physical calculator.
Dependencies: math
Suggested calculator name: FRUSTVOL — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Browser preview

Try frustum volume

This browser preview calculates volume from height and two base areas. The TI program also solves the inverse modes.

Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

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Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Frustum Volume for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def positive_number(prompt):
    """Require a positive finite number."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def show_answer(name, value, unit):
    print()
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def frustum_volume(h, a1, a2):
    """Calculate frustum volume."""
    return (
        h / 3 *
        (a1 + a2 + sqrt(a1 * a2))
    )


def solve_missing_area(volume, height, known_area):
    """Solve one base area when the other is known."""

    k = 3 * volume / height

    inside = 4 * k - 3 * known_area

    if inside < 0:
        return None

    root_area = (
        -sqrt(known_area) +
        sqrt(inside)
    ) / 2

    if root_area < 0:
        return None

    return root_area ** 2


def main():
    duckiedai_intro("FRUSTUM VOLUME")

    print("FRUSTUM VOLUME")
    print()
    print("V = h/3 *")
    print("(A1+A2+sqrt(A1*A2))")
    print()
    print("A1 = base area 1")
    print("A2 = base area 2")
    print("h  = height")
    print()
    print("What do you need?")
    print()
    print("1. Volume")
    print("2. Height")
    print("3. Base area A1")
    print("4. Base area A2")
    print()

    choice = input("Choose 1-4: ")

    print()

    # ==========================================
    # 1. SOLVE VOLUME
    #
    # V = h/3(A1+A2+sqrt(A1*A2))
    # ==========================================

    if choice == "1":

        h = positive_number(
            "Height: "
        )

        a1 = positive_number(
            "Base area A1: "
        )

        a2 = positive_number(
            "Base area A2: "
        )

        volume = frustum_volume(
            h, a1, a2
        )

        print()
        print("Using:")
        print("V = h/3 *")
        print("(A1+A2+sqrt(A1*A2))")

        show_answer(
            "Volume",
            volume,
            "cubic units"
        )

    # ==========================================
    # 2. SOLVE HEIGHT
    #
    # h = 3V /
    # (A1+A2+sqrt(A1*A2))
    # ==========================================

    elif choice == "2":

        volume = positive_number(
            "Volume: "
        )

        a1 = positive_number(
            "Base area A1: "
        )

        a2 = positive_number(
            "Base area A2: "
        )

        denominator = (
            a1 +
            a2 +
            sqrt(a1 * a2)
        )

        h = (
            3 * volume /
            denominator
        )

        print()
        print("Using:")
        print("V = h/3 *")
        print("(A1+A2+sqrt(A1*A2))")
        print()
        print("Rearranged:")
        print("h = 3V /")
        print("(A1+A2+sqrt(A1*A2))")

        show_answer(
            "Height",
            h,
            "units"
        )

    # ==========================================
    # 3. SOLVE A1
    # ==========================================

    elif choice == "3":

        volume = positive_number(
            "Volume: "
        )

        h = positive_number(
            "Height: "
        )

        a2 = positive_number(
            "Known area A2: "
        )

        a1 = solve_missing_area(
            volume,
            h,
            a2
        )

        if a1 is None:

            print()
            print("NO VALID RESULT")
            print()
            print("Check volume,")
            print("height, and area.")

        else:

            print()
            print("Using:")
            print("V = h/3 *")
            print("(A1+A2+sqrt(A1*A2))")
            print()
            print("Solved for A1.")

            show_answer(
                "A1",
                a1,
                "square units"
            )

    # ==========================================
    # 4. SOLVE A2
    # ==========================================

    elif choice == "4":

        volume = positive_number(
            "Volume: "
        )

        h = positive_number(
            "Height: "
        )

        a1 = positive_number(
            "Known area A1: "
        )

        a2 = solve_missing_area(
            volume,
            h,
            a1
        )

        if a2 is None:

            print()
            print("NO VALID RESULT")
            print()
            print("Check volume,")
            print("height, and area.")

        else:

            print()
            print("Using:")
            print("V = h/3 *")
            print("(A1+A2+sqrt(A1*A2))")
            print()
            print("Solved for A2.")

            show_answer(
                "A2",
                a2,
                "square units"
            )

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Frustum Volume for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def positive_number(prompt):
"""Require a positive finite number."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def show_answer(name, value, unit):
print()
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def frustum_volume(h, a1, a2):
"""Calculate frustum volume."""
return (
h / 3 *
(a1 + a2 + sqrt(a1 * a2))
)
def solve_missing_area(volume, height, known_area):
"""Solve one base area when the other is known."""
k = 3 * volume / height
inside = 4 * k - 3 * known_area
if inside < 0:
return None
root_area = (
-sqrt(known_area) +
sqrt(inside)
) / 2
if root_area < 0:
return None
return root_area ** 2
def main():
duckiedai_intro("FRUSTUM VOLUME")
print("FRUSTUM VOLUME")
print()
print("V = h/3 *")
print("(A1+A2+sqrt(A1*A2))")
print()
print("A1 = base area 1")
print("A2 = base area 2")
print("h = height")
print()
print("What do you need?")
print()
print("1. Volume")
print("2. Height")
print("3. Base area A1")
print("4. Base area A2")
print()
choice = input("Choose 1-4: ")
print()
# ==========================================
# 1. SOLVE VOLUME
#
# V = h/3(A1+A2+sqrt(A1*A2))
# ==========================================
if choice == "1":
h = positive_number(
"Height: "
)
a1 = positive_number(
"Base area A1: "
)
a2 = positive_number(
"Base area A2: "
)
volume = frustum_volume(
h, a1, a2
)
print()
print("Using:")
print("V = h/3 *")
print("(A1+A2+sqrt(A1*A2))")
show_answer(
"Volume",
volume,
"cubic units"
)
# ==========================================
# 2. SOLVE HEIGHT
#
# h = 3V /
# (A1+A2+sqrt(A1*A2))
# ==========================================
elif choice == "2":
volume = positive_number(
"Volume: "
)
a1 = positive_number(
"Base area A1: "
)
a2 = positive_number(
"Base area A2: "
)
denominator = (
a1 +
a2 +
sqrt(a1 * a2)
)
h = (
3 * volume /
denominator
)
print()
print("Using:")
print("V = h/3 *")
print("(A1+A2+sqrt(A1*A2))")
print()
print("Rearranged:")
print("h = 3V /")
print("(A1+A2+sqrt(A1*A2))")
show_answer(
"Height",
h,
"units"
)
# ==========================================
# 3. SOLVE A1
# ==========================================
elif choice == "3":
volume = positive_number(
"Volume: "
)
h = positive_number(
"Height: "
)
a2 = positive_number(
"Known area A2: "
)
a1 = solve_missing_area(
volume,
h,
a2
)
if a1 is None:
print()
print("NO VALID RESULT")
print()
print("Check volume,")
print("height, and area.")
else:
print()
print("Using:")
print("V = h/3 *")
print("(A1+A2+sqrt(A1*A2))")
print()
print("Solved for A1.")
show_answer(
"A1",
a1,
"square units"
)
# ==========================================
# 4. SOLVE A2
# ==========================================
elif choice == "4":
volume = positive_number(
"Volume: "
)
h = positive_number(
"Height: "
)
a1 = positive_number(
"Known area A1: "
)
a2 = solve_missing_area(
volume,
h,
a1
)
if a2 is None:
print()
print("NO VALID RESULT")
print()
print("Check volume,")
print("height, and area.")
else:
print()
print("Using:")
print("V = h/3 *")
print("(A1+A2+sqrt(A1*A2))")
print()
print("Solved for A2.")
show_answer(
"A2",
a2,
"square units"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: FRUSTVOL.py
Size: 5989 bytes
SHA-256: 843d2b627eedddda839b21978ad6b94af9db20adee8b489f96886e5c4adc8f4e

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. FRUSTVOL is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

Availability does not mean a teacher, school, or exam permits this program. Follow the applicable rules.

Version history

1.0.0 — current version, published 2026-09-24. Download this reviewed version

Any source change requires a new immutable version and digest. Historical downloads remain available only while their review records remain valid.

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