Geometry Geometric Modeling Applications Worksheet (PDF)

Geometry math worksheet: Geometric Modeling Applications – Maths PDF

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This modeling practice worksheet for Geometry covers geometric modeling applications (Common Core G-MG.A.1, G-MG.A.2, G-MG.A.3), with a free PDF to print.

These 20 problems practice modeling with shapes, density and design problems (Common Core G-MG.A.1 to G-MG.A.3). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are applications with cans, fences, tanks, concrete and honeycombs.

Geometry · Common Core State Standards: G-MG.A.1, G-MG.A.2, G-MG.A.3

Modeling practice worksheet: exercises 1 to 10

Exercise 1 – Can as a cylinder

A soup can is modeled by a cylinder.

A soup can has diameter 6.6 cm and height 11.5 cm. Model it as a cylinder and find its volume to the nearest tenth.

Exercise 2 – A log

A log is modeled as a cylinder with diameter 24 inches and length 20 feet. Find its volume in cubic feet to the nearest tenth. (Convert first.)

Exercise 3 – Density of aluminum

Aluminum block.

An aluminum block is 10 cm by 8 cm by 5 cm and has mass 1,080 g. Find its density.

Exercise 4 – Mass of a lead cylinder

A lead cylinder has radius 2 cm and height 10 cm. Lead has density 11.34 g per cm³. Find the mass to the nearest gram.

Exercise 5 – Population density

Maple Falls has 31,250 people on 12.5 square miles. Find its population density.

Exercise 6 – Population from density

A suburb has a population density of 4,200 people per square mile and covers 6.5 square miles. Estimate its population.

Exercise 7 – Painting a room

Room 12 ft by 10 ft with 8 ft walls.

Jamal paints the four walls of a room 12 ft by 10 ft with 8-ft walls, ignoring doors and windows. One gallon covers 350 square feet and costs $32. Find the wall area, the gallons needed (round up to a whole number) and the cost of one coat.

Exercise 8 – Weight of a beam

A pine beam is 4 inches by 6 inches by 12 feet. Pine weighs 35 pounds per cubic foot. Find the volume in cubic feet and the weight of the beam.

Exercise 9 – Gallons in a tank

A soup can is modeled by a cylinder.

A cylindrical tank has radius 4 feet and height 10 feet. One cubic foot holds about 7.48 gallons. How many gallons does the tank hold, to the nearest 10 gallons?

Exercise 10 – Concrete slab

A patio slab is 20 ft by 12 ft and 4 inches thick. Concrete costs $145 per cubic yard. Find the volume in cubic yards (to the nearest hundredth) and the cost to the nearest dollar.

Exercises 11 and up

Exercise 11 – Fence design

Fence on three sides of a rectangular garden next to a barn.

Maya has 120 feet of fence to enclose three sides of a rectangular garden next to a barn. She compares widths of 25, 30 and 35 feet. Find the length and area of each design and choose the largest area.

Exercise 12 – Minimum height of a tank

A cylindrical tank with radius 5 feet must hold at least 1,000 cubic feet. Find the smallest height to the nearest tenth of a foot.

Exercise 13 – Material for a can

A can has radius 3.3 cm and height 11.5 cm. Find the surface area of the metal to the nearest square centimeter.

Exercise 14 – Painting a tank

The curved side of a cylindrical tank (radius 4 ft, height 10 ft) is painted. Paint covers 250 square feet per gallon. Find the area and the gallons to buy (round up).

Exercise 15 – Attic volume

Attic as a pyramid.

A roof forms a pyramid with a 30 ft by 20 ft rectangular base and height 8 ft. Find the volume of air in the attic.

Exercise 16 – Basketball

A ball is modeled by a sphere.

A basketball has diameter 9.5 inches. Model it as a sphere and find its volume to the nearest tenth.

Exercise 17 – Grass seed

A 60 ft by 90 ft lot has a 40 ft by 30 ft house on it. Grass seed is used at 1 pound per 400 square feet on the part without the house. How many pounds are needed?

Exercise 18 – Honeycomb cell

A honeycomb cell is modeled by a regular hexagon.

A honeycomb cell is a regular hexagon with side 3 mm. Find its area to the nearest tenth, using $A = \frac{3\sqrt{3}}{2}s^{2}$.

Exercise 19 – Tennis ball can

Can holding three balls.

A tennis ball can is a cylinder of height $6r$ that holds three balls of radius $r$. Find the fraction of the can’s volume that is empty.

Exercise 20 – Best pizza value

A 10-inch pizza costs $8 and a 14-inch pizza costs $14 (diameters). Compare the area per dollar and decide which is the better value.

Key facts behind this modeling practice worksheet

Key facts

A model represents a real object with a simple shape, for example a can as a cylinder.
Density = amount / area or volume (people per square mile, grams per cubic centimeter).
Mass = density x volume.
Design problems have constraints such as fixed fencing, minimum volume or a cost limit.
State answers with units and check they are reasonable.

How to use this modeling practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the modeling practice worksheet as a PDF with the button below and keep it with your notes.

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