Level 2 · Intermediate ← Back to lesson

Building and Checking a Geometric Model: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A canvas cover is modeled as a rectangle 2.2 m by 90 cm plus a nonoverlapping triangle. The triangle shares the full 2.2 m side, and its perpendicular height is 40 cm. What is the model area?

Answer choices for question 1 A $1.98\text{ m}^2$ B $2.86\text{ m}^2$ C $2.42\text{ m}^2$ D $24.2\text{ m}^2$
2

A square tile side is reported as 44 cm to the nearest centimeter. Ties round to the larger report. Which is the measurement interval for side length $s$ in centimeters?

Answer choices for question 2 A $43.5\le s<44.5$ B $43.5<s\le44.5$ C $43\le s<45$ D $44\le s<44.5$
3

A rectangular label has fixed height 6 cm and width $w$ between 7.2 and 7.6 cm, with both endpoints allowed. What is its area range in square centimeters?

Answer choices for question 3 A $43.2<A<45.6$ B $13.2\le A\le13.6$ C $44.4\le A\le45.6$ D $43.2\le A\le45.6$
4

A sheet has a fixed area of 30 square meters before a vent is cut. The vent is a rectangle with fixed length 1.5 m and width between 0.4 and 0.6 m, inclusive. What is the least remaining area?

Answer choices for question 4 A $29.4\text{ m}^2$ B $29.1\text{ m}^2$ C $29.25\text{ m}^2$ D $30.9\text{ m}^2$
5

Two rectangular panels are disjoint. They share a common width $w$ . Their fixed lengths are 4 m and 1.25 m. If $w$ is at least 2.1 m and less than 2.3 m, which is the upper bound on their total area, and can it occur?

Answer choices for question 5 A 12.075 square meters, excluded B 12.075 square meters, included C 11.825 square meters, excluded D 11.025 square meters, included
6

A straight planter is modeled as a rectangular prism. Its dimensions are 2.3 m, 82 cm, and 47 cm. Which is the closest rough estimate of its volume in cubic meters?

Answer choices for question 6 A $9\text{ m}^3$ B $90\text{ m}^3$ C $0.9\text{ m}^3$ D $900\text{ m}^3$
7

An aisle model treats a 7.8 m by 3.5 m space as a rectangle. A separately surveyed grid reports 26.8 square meters for the same area. What is the difference, model area minus grid estimate?

Answer choices for question 7 A $-0.5\text{ m}^2$ B $0.5\text{ m}^2$ C $1.3\text{ m}^2$ D $3.3\text{ m}^2$
8

A window model uses a rectangle and a triangle with its base on one full horizontal side of the rectangle. The two parts meet along that side and do not overlap. To find the total model area, what triangle measurement is needed along with the shared side length?

Answer choices for question 8 A The slanted distance from the tip to the closest corner B The sum of the two slanted sides C The length of the longer slanted side alone D The perpendicular distance from the tip to the line of the shared side
9

A shape model predicts an area from 18.1 to 19.2 square meters, including both endpoints. Which separately surveyed area is consistent with that range?

Answer choices for question 9 A $19.21\text{ m}^2$ B $18.09\text{ m}^2$ C $19.2\text{ m}^2$ D $20.1\text{ m}^2$
10

A positive length is reported as 6.4 m to the nearest tenth, with ties going to the larger report. Which statement about readings before rounding is true?

Answer choices for question 10 A 6.35 m and 6.45 m both round to 6.4 m. B 6.35 m and 6.449 m both round to 6.4 m. C 6.349 m and 6.40 m both round to 6.4 m. D 6.45 m and 6.451 m both round to 6.4 m.
11

A dock model counts an area of 13.4 square meters. Inspection finds that the model left out a fixed triangular extension with base 1.8 m and perpendicular height 0.6 m. What is the revised model area after adding it?

Answer choices for question 11 A $12.86\text{ m}^2$ B $14.48\text{ m}^2$ C $15.2\text{ m}^2$ D $13.94\text{ m}^2$
12

A hall plan treats its measured length as lying in an interval and stipulates an exact width of 4 m for the model. What assumption allows you to multiply both length endpoints by 4 to find the area bounds?

Answer choices for question 12 A The hall is modeled as a rectangle with the same fixed width at every allowed length. B The actual width has the same uncertainty as the length. C The length and width always change together. D The endpoints of the length interval are both excluded.

← Back to lesson