Question

The isometric projection of a sphere of radius 'R' is drawn using radius equal to:

• A. Isometric R
• B. $0.5 \, R$
• C. $2 \, R$
• D. True R

Hint:

This is a classic board exam question! Always remember:
• Radius of the projected circle = True $R$
• Height of the center of the sphere = Isometric $R$ (or isometric distance from base)

Answer 1

The Correct Option is D

Step 1: Understanding Sphere Projections in Isometric Views:
A sphere is perfectly symmetrical in three dimensions. When viewed from any direction, its orthogonal projection is always a circle of radius equal to the true radius $R$ of the sphere.

Step 2: Drawing the Boundary of a Projected Sphere:
In isometric projection:
• The distance from the center of the sphere to any point on its outer boundary (its silhouette/contour) is projected without any foreshortening because the outer boundary is perpendicular to the line of sight.
• Consequently, the outer boundary of a sphere in an isometric drawing is always drawn as a perfect circle of radius equal to the True Radius ($R$) of the sphere.

Step 3: Positioning the Center of the Sphere:
Note that the position of the center of the sphere from the ground or its resting point *is* an isometric distance, and is measured using the Isometric Scale (i.e., $\text{Isometric height} = 0.816 \times \text{True height}$). However, once the center is located, the boundary circle of the sphere is drawn using its True Radius ($R$). Therefore, option (D) is correct.