NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.1
Question 14

Question.  14

A medicine capsule is a cylinder of diameter 0.5 cm with two hemispherical ends. The length of the capsule is 2 cm. Its capacity is

(A)

0.36 cm³

(B)

0.35 cm³

(C)

0.34 cm³

(D)

0.33 cm³

Detailed Answer with Explanation:

Step 1: The capsule is made of a cylinder with two hemispherical ends.

Step 2: Diameter of capsule = 0.5 cm.
Radius \(r = \dfrac{0.5}{2} = 0.25\,\text{cm}\).

Step 3: Total length of capsule = 2 cm.
The two hemispherical ends together make one full sphere of radius 0.25 cm.
So, cylindrical length \(h = 2 - 2r = 2 - 0.5 = 1.5\,\text{cm}\).

Step 4: Volume of cylinder = \(\pi r^2 h\).
\(= 3.1416 \times (0.25)^2 \times 1.5\).
\(= 3.1416 \times 0.0625 \times 1.5 = 0.2945\,\text{cm}^3\).

Step 5: Volume of sphere = \(\dfrac{4}{3}\pi r^3\).
\(= \dfrac{4}{3} \times 3.1416 \times (0.25)^3\).
\(= \dfrac{4}{3} \times 3.1416 \times 0.015625\).
\(= 0.0654\,\text{cm}^3\).

Step 6: Total volume = volume of cylinder + volume of sphere.
\(= 0.2945 + 0.0654 = 0.3599 \approx 0.36\,\text{cm}^3\).

Final Answer: The capacity of the capsule is 0.36 cm³ (Option A).

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