Understanding Paper Sizes: A3 Dimensions in mm

The question asks for the standard dimensions of an A3 sheet of paper in millimeters, as defined by the Indian Standard Institution (ISI). Paper size standards like those used by ISI are typically based on international norms, most commonly the ISO 216 standard.

The ISO 216 Standard and the A Series

The ISO 216 standard defines the A series of paper sizes. This standard is based on a few key principles:

• All paper sizes in the series have an aspect ratio (ratio of the longer side to the shorter side) of \(1:\sqrt{2}\).
• Each subsequent size in the series is obtained by cutting the sheet of the previous size in half along its longer side.

The base size is A0, which has an area of 1 square meter. Its dimensions are approximately \(1189 \text{ mm} \times 841 \text{ mm}\). Let's derive the sizes:

• A0: \(1189 \text{ mm} \times 841 \text{ mm}\) (Area is close to \(1 \text{ m}^2\))
• A1: Obtained by halving the longer side of A0 (1189 mm). Dimensions become \(841 \text{ mm} \times (1189/2) \text{ mm} \approx 841 \text{ mm} \times 594 \text{ mm}\). So, A1 is \(841 \text{ mm} \times 594 \text{ mm}\).
• A2: Obtained by halving the longer side of A1 (841 mm). Dimensions become \(594 \text{ mm} \times (841/2) \text{ mm} \approx 594 \text{ mm} \times 420 \text{ mm}\). So, A2 is \(594 \text{ mm} \times 420 \text{ mm}\).
• A3: Obtained by halving the longer side of A2 (594 mm). Dimensions become \(420 \text{ mm} \times (594/2) \text{ mm} = 420 \text{ mm} \times 297 \text{ mm}\). So, A3 is \(420 \text{ mm} \times 297 \text{ mm}\).

These dimensions \(420 \times 297 \text{ mm}\) maintain the \(1:\sqrt{2}\) aspect ratio (\(420 / 297 \approx 1.414\) which is close to \(\sqrt{2} \approx 1.414\)).

Comparing with Options

Let's compare the calculated standard dimensions with the provided options:

• Option 1: \(1189 \times 841 \text{ mm}\) - This matches the standard dimensions of an A0 sheet.
• Option 2: \(297 \times 210 \text{ mm}\) - This matches the standard dimensions of an A4 sheet (half of A3).
• Option 3: \(841 \times 594 \text{ mm}\) - This matches the standard dimensions of an A1 sheet.
• Option 4: \(420 \times 297 \text{ mm}\) - This matches the standard dimensions of an A3 sheet.

Based on the standard derivation and comparison with the options, the size of an A3 sheet according to ISI (following ISO 216) is \(420 \times 297 \text{ mm}\).

Revision Table: Standard Paper Sizes

Additional Information on Paper Size Standards

Beyond the A series, the ISO 216 standard also defines the B series, and ISO 269 defines the C series. These series also follow the \(1:\sqrt{2}\) aspect ratio and are related to the A series:

• B Series: Used for posters, books, and other applications where A series sizes might not be suitable. The dimensions of a B(n) size are the geometric mean of A(n) and A(n-1). For example, B1 is the geometric mean of A1 and A0. B0 is \(1000 \times 1414 \text{ mm}\).
• C Series: Primarily used for envelopes. The dimensions of a C(n) size are the geometric mean of A(n) and B(n). A C4 envelope is sized to fit an A4 sheet unfolded, and a C5 envelope fits an A5 sheet (or an A4 sheet folded once).

Understanding these standard paper sizes is important in various fields, including printing, design, engineering drawing, and office use.