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2023 AMC 10B Problem 4

2023 AMC 10B Problem 4AMC 10 Step by Step

Name: Date: September 13, 2026

Sets, Estimation & Miscellaneous · difficulty 1 of 5 · about 2 min · position P1-10

Jackson's paintbrush makes a narrow strip with a width of $6.5$ millimeters. Jackson has enough paint to make a strip $25$ meters long. How many square centimeters of paper could Jackson cover with paint?

A)
$162{,}500$
B)
$162.5$
C)
$1{,}625$
D)
$1{,}625{,}000$
E)
$16{,}250$

Answer

Key insight

Convert both dimensions to centimeters first: 6.5 mm = 0.65 cm and 25 m = 2500 cm, then multiply to get 1625 square centimeters.

Solution

The painted strip is a long thin rectangle. Convert both sides to centimeters before multiplying:
$6.5 \text{ mm} = 0.65 \text{ cm}, \qquad 25 \text{ m} = 2500 \text{ cm}.$
The area is
$0.65 \times 2500 = 1625 \text{ cm}^2.$

The answer is $\boxed{\textbf{(C)}\ 1{,}625}$ .

Why this works

Area in a target unit is easiest when every length is expressed in that unit first; then the area formula needs no further conversion. Converting the area afterward (e.g. from mm $^2$ to cm $^2$ by dividing by $100$ , not $10$ ) is where most errors occur.

Alternative approach

Sanity check the magnitude: $0.65$ cm is a bit over half a centimeter, and $2500$ cm of that width is roughly $2500/2 \approx 1250$ to $2500$ cm $^2$ . Only $1{,}625$ is in that range.

The trap

Slipping a factor of 10 in one of the conversions; every answer choice differs from the others only by powers of 10.

Common mistakes

Slipping a factor of 10 in one of the conversions; every answer choice differs from the others only by powers of 10.
Multiplying $6.5 \times 2500 = 16{,}250$ in mixed units (mm and cm) and forgetting to convert the width.

Techniques

Set up the equation/formula and compute; no special trick needed