Level 3 · Challenge ← Back to lesson

Building and Checking a Geometric Model: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A 9 m long floor has a 2 m long end strip removed across the full width $w$ . The width ranges from 4.3 to 4.7 m, inclusive. What is the least remaining area?

Answer choices for question 1 A $29.3\text{ m}^2$ B $32.9\text{ m}^2$ C $38.7\text{ m}^2$ D $30.1\text{ m}^2$
2

A cover model subtracts a rectangular vent from a fixed 22-square-meter top. The vent length is fixed at 2 m. Its width is reported as 1.8 m to the nearest tenth, with ties going to the larger report. Which describes the least end of the remaining area range?

Answer choices for question 2 A The minimum is 18.3 square meters and is attained. B The lower bound is 18.3 square meters and is excluded. C The lower bound is 18.5 square meters and is excluded. D The minimum is 18.4 square meters and is attained.
3

A mat model has a fixed length of 4.5 m and width from 1.6 to 1.8 m, inclusive. A second method reports 8.6 square meters for the same mat. Which next step is supported?

Answer choices for question 3 A Accept 8.6 square meters as covered by the model range. B Conclude the width measurement is the sole source of error. C Recheck the width data, shape assumption, and second method. D Raise the model's upper bound to 8.6 without revisiting the inputs.
4

A curb cut has a lower model area of 5.6 square meters and upper model area of 6.4 square meters, both attained. A revised model adds a fixed 0.35-square-meter side patch. What is the new model interval?

Answer choices for question 4 A $5.95\le A\le6.75$ B $5.25\le A\le6.05$ C $5.6\le A\le6.75$ D $5.95<A<6.75$
5

An outer rectangle has fixed length 8 m. Its width is at least 4.05 m and less than 4.15 m. A rectangular recess of fixed length 3 m has width at least 0.65 m and less than 0.75 m. The widths vary independently and the recess always fits. What are the bounds on the remaining area in square meters?

Answer choices for question 5 A $30.15\le A<31.25$ B $30.45\le A<30.95$ C $30.15<A<31.25$ D $30.45<A<30.95$
6

A footbridge model uses a rectangle to predict the deck area. It closely matches a separate area survey. The builder wants to use the same model to locate holes along the deck's curved railing. What is supported by the survey?

Answer choices for question 6 A The area agreement fixes the correct position of every hole. B The deck must have straight sides. C The rectangle can locate the holes once its area is rounded. D The survey supports the area estimate. The hole locations need a check of the railing shape.
7

A 1.7 m long, 65 cm wide, 30 cm tall block is modeled as a rectangular prism. Which computation gives its volume in cubic meters?

Answer choices for question 7 A $1.7(0.65)(0.30)$ B $1.7(65)(30)$ C $1.7(0.65)(30)$ D $1.7(65)(0.30)$
8

A bench seat model has fixed depth 38 cm. The length report of 1.2 m is rounded to the nearest tenth of a meter, with ties going to the larger report. Which describes model area in square meters?

Answer choices for question 8 A $43.7\le A<47.5$ B $0.437\le A<0.475$ C $0.456\le A<0.475$ D $0.437<A\le0.475$
9

A team measures a path width with a damaged tape and rounds its reading to the nearest tenth. What does the interval from that rounding rule bound?

Answer choices for question 9 A The true width even if the damaged tape reads incorrectly B The error caused by the damaged tape C The area omitted by the path model D The possible unrounded tape reading that led to the report
10

A model for the area of a flat splash pad predicts 28 to 29 square meters. A survey reports 30.7 to 31.1 square meters. A roughly triangular extension outside the model has base 3.4 m and perpendicular height 1.6 m. Treat its area as fixed and add it to the model. Which conclusion follows?

Answer choices for question 10 A The revised interval is 30.72 to 31.72 square meters, which overlaps the survey. B The revised interval is 25.28 to 26.28 square meters, below the survey. C The revised interval is 33.44 to 34.44 square meters, above the survey. D The revised interval is 30.72 to 31.72 square meters, which contains every survey value.
11

A greenhouse model treats its side wall as a rectangle plus a triangle. Both parts use the same base width. A second team measures the total wall area directly and falls within the predicted bounds. Which would give useful new evidence about the triangular part of the model?

Answer choices for question 11 A Recalculate the same total area using the same two widths. B Measure the area of the upper part separately. C Add more decimal places to the rectangle area. D Record the already observed total a second time.
12

A technician reports that a rectangular intake has area 0.1749 square meters from two rounded length readings. A calculation with convenient nearby numbers gave about 0.18 square meters. What does the rough estimate support?

Answer choices for question 12 A Every digit in 0.1749 measures the real intake exactly. B The intake has straight sides. C The calculated area has a plausible size. D The estimate makes a separate check of the actual area unnecessary.

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