NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.1
Question 16

Question.  16

A right circular cylinder of radius \(r\) cm and height \(h\) cm (with \(h>2r\)) just encloses a sphere. The diameter of the sphere is

(A)

\(r\) cm

(B)

\(2r\) cm

(C)

\(h\) cm

(D)

\(2h\) cm

Detailed Answer with Explanation:

Step 1: A sphere is a perfectly round ball. If it is placed inside a cylinder, it will touch the cylinder from all sides.

Step 2: The widest part of the sphere is its diameter. This diameter must be the same as the inner width of the cylinder for the sphere to fit exactly.

Step 3: The inner width of the cylinder is measured across its circular base. That width is equal to the diameter of the base circle.

Step 4: The diameter of the base circle of the cylinder is \(2r\) (since radius is \(r\), diameter = \(2 \times r\)).

Step 5: Therefore, the diameter of the sphere = diameter of the cylinder’s base = \(2r\).

Final Answer: The diameter of the sphere is \(2r\) cm. (Option B)

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 12: Surface Areas & Volumes – Exercise 12.1 | Detailed Answers