Worksheet

Makerspace Lending: Circle Specs

Apply circle area and circumference formulas to library makerspace kits, then explain how the formulas are related.

Grade 7MathInteractive · Printable

Aligned to7.G.B.4

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
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Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Short answer

About this worksheet

What students practice

Students calculate circle area and circumference from radius, diameter, or other circle measurements.
Students apply circle formulas to material quantities for lending kits.
Students explain how rearranging circle sectors connects area to circumference.

How to use

Use after introducing circle formulas. Allow calculators, and have students show their setup on scratch paper before comparing the formulas in the final section.

Curriculum

Common Core standard covered

7.G.B.4

Know and use the formulas for the area and circumference of a circle, and informally explain how they are related.

Preview

OwlSheets.com

Name Date

Makerspace Lending: Circle Specs

Use circle measurements to prepare tools and kits for checkout.

Check the Measurement Labels

The library lends makerspace tools and kits. Use π = 3.14 unless a question asks for an answer in terms of π. Do not round your calculations.

A circular cutting mat needs protective tape around its edge. Its diameter is d centimeters. Which formula gives the tape length C?

A. C = πd
B. C = 2πd
C. C = πd²
D. C = πd ÷ 2

A circular template in a tracing kit has a radius of 7.5 cm.

What is its circumference? cm

A circular pressing pad has a diameter of 14 cm. A replacement cover must cover exactly one circular face.

What area must the cover have? cm²

A circular stencil has a circumference of 37.68 cm. Its diameter label is missing.

What diameter belongs on the label? cm

Jalen calculates the area of a circular magnifier with a diameter of 10 cm as 3.14 × 10² = 314 cm². Which correction should he make?

A. Use 3.14 × 10 = 31.4 cm² instead.
B. Use 3.14 × 5² = 78.5 cm² instead.
C. Use 2 × 3.14 × 10 = 62.8 cm² instead.
D. Use 3.14 × 20² = 1,256 cm² instead.

Prepare the Lending Kits

Choose the measurements needed for each task. Use π = 3.14, and ignore seams, overlap, and waste unless stated.

One kit contains the circular mats listed below. Each mat needs a cover on one face.

Mats in One Kit
Mat size	Radius (cm)	Number of mats
Small	5	2
Large	10	1

What is the total area of cover material needed? cm²

A repair kit has two circular spool flanges. Each flange has a diameter of 18 cm. Protective tape goes once around the outside edge of each flange.

How much tape is needed in all? cm

A ring-shaped foam insert holds a tool securely. Its outer circle has radius 9 cm, and its circular opening has radius 6 cm.

What is the area of the foam ring? cm²

A circular sanding pad has an area of 200.96 cm². The checkout record needs its radius.

What is the radius? cm

10.

Priya has 200 cm of edge tape. She must tape once around each of three circular work mats with diameter 20 cm. Which statement is correct?

A. The tape is not enough; she needs 742 cm more.
B. The tape is enough, with 105.8 cm left.
C. The tape is not enough; she needs 176.8 cm more.
D. The tape is enough, with 11.6 cm left.

Connect Area and Circumference

Compare how the two measurements change, then explain their connection.

11.

A new circular template has twice the radius of an older template. How do its circumference and area compare with the older template?

A. Its circumference doubles, and its area doubles.
B. Its circumference quadruples, and its area doubles.
C. Its circumference doubles, and its area quadruples.
D. Its circumference quadruples, and its area quadruples.

12.

A circular grip pad has a circumference of 31.4 cm. A librarian needs its area to order a replacement sheet. Use π = 3.14.

What is the pad's area? cm²

13.

A circular template has radius 6 cm. Which pair gives its exact circumference and area in terms of π?

A. Circumference: 12π cm; area: 36π cm²
B. Circumference: 12π cm; area: 12π cm²
C. Circumference: 36π cm; area: 12π cm²
D. Circumference: 6π cm; area: 36π cm²

14.

A demonstration kit has a paper circle cut into many narrow, equal sectors. Students alternate the sectors, pointing up and down, to make a shape that is nearly a rectangle. The shape's height is about the circle's radius r, and its base is about half the circle's circumference C. Explain why this shows that A = (C ÷ 2) × r, and use C = 2πr to connect this result to A = πr².