Title: Need Help Solving a 3D Geometry Problem Involving Architectural Volume Calculations

Question

Description: I'm working on a design project and need to calculate the total volume of an irregular 3D architectural structure. The building is composed of: A rectangular base: 20m x 15m x 3m A cylindrical tower on top: radius 5m, height 12m A half-sphere dome on top of the cylinder I need help with:

Calculating the volume of each section Combining the volumes into a total Explaining the formulas used A clear step-by-step solution would be best. Attached is a sketch of the structure.

GB_Megazord · Answer

muhammadazimhafifi · Answer

"i hope you’ll consider buying my answer on minasei, and i truly hope it meets your expectations."

ConsQuickAnswers · Answer

step 1: volume of the rectangular base formula:

vrect=length×width×heightv_{ ext{rect}} = ext{length} imes ext{width} imes ext{height}

given: length = 20 m width = 15 m height = 3 m calculation:

m3v_{ ext{rect}} = 20 imes 15 imes 3 = 900\ ext{m}^3

step 2: volume of the cylindrical tower formula:

vcyl=πr2hv_{ ext{cyl}} = \pi r^2 h

given: radius = 5 m height = 12 m calculation:

m3v_{ ext{cyl}} = \pi (5)^2 (12) = \pi imes 25 imes 12 = 300\pi \approx 942.48\ ext{m}^3

step 3: volume of the half-spherical dome formula for a full sphere:

vsphere=43πr3v_{ ext{sphere}} = \frac{4}{3}\pi r^3

since this is a half-sphere, the volume becomes:

vhalf-sphere=12×43πr3=23πr3v_{ ext{half-sphere}} = \frac{1}{2} imes \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3

given: radius = 5 m calculation:

m3v_{ ext{half-sphere}} = \frac{2}{3} \pi (5)^3 = \frac{2}{3} \pi (125) = \frac{250}{3} \pi \approx 261.80\ ext{m}^3

step 4: total volume of the structure add the volumes of all three components: rectangular base: 900 m³ cylindrical tower: ≈ 942.48 m³ half-spherical dome: ≈ 261.80 m³ total volume:

m3v_{ ext{total}} = 900 + 942.48 + 261.80 = 2104.28\ ext{m}^3

summary of formulas used shapeformuladescriptionrectangular prism

v = l \times w \times h

volume of the rectangular basecylinder

\pi r^2 h

volume of the cylindrical sectionhalf-sphere

\frac{2}{3} \pi r^3

volume of the dome-shaped top final answer: the total volume of the structure is approximately 2104.28 m³.

mariapaula93 · Answer

the total volume of the structure can be found by adding the volumes of the three parts: the rectangular base, the cylindrical tower, and the half-sphere dome. the rectangular base has volume

vrect=length×width×heightv_{ ext{rect}} = ext{length} imes ext{width} imes ext{height}

.the cylinder has volume

π r^{2} h = π \times 5^{2} \times 12 = 300 π \approx 942 m^{3}

.the half-sphere dome has volume

\frac{2}{3} π r^{3} = \frac{2}{3} π \times 5^{3} = \frac{250}{3} π \approx 262 m^{3}

. adding them together:

900 + 942 + 262 \approx 2, 104 m^{3}

so, the total volume of the building is about 2,104 cubic meters.

Category:	Architecture
Offered Price:	$10.00
Due Date:	31 July 2025, 02:07
Added:	31 July 2025, 00:13

Price:	10.00
Added:	31 July 2025, 04:42
Attachments:	1 file, 450 words
Buyers:	No Buyers Yet

Price:	8.00
Added:	31 July 2025, 05:10
Words:	16 words
Attachments:	3 files, 208 words
Buyers:	No Buyers Yet

Price:	7.00
Added:	31 July 2025, 19:32
Words:	221 words
Attachments:	1 file, 250 words
Buyers:	No Buyers Yet

Price:	6.50
Added:	19 August 2025, 22:25
Words:	60 words
Buyers:	No Buyers Yet

Title: Need Help Solving a 3D Geometry Problem Involving Architectural Volume Calculations

Secure Payment

We let the professionals process your money

Secure Payment

We let the professionals process your money

Secure Payment

We let the professionals process your money

Secure Payment

We let the professionals process your money

Have a similar question?