1 View

Question : The largest possible right circular cylinder is cut out from a wooden cube of edge 7 cm. Find the volume of the cube (in cm3) left over after cutting the cylinder. (Use $\pi=\frac{22}{7}$)

Option 1: 73.5

Option 2: 63.5

Option 3: 87.5

Option 4: 67.5


Team Careers360 11th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

Correct Answer: 73.5


Solution : The largest possible right circular cylinder that can be cut out from a cube will have its diameter equal to the edge of the cube.
Given that the edge of the cube is 7 cm, the radius $r$ of the cylinder is $\frac{7}{2}$ cm and the height $h$ of the cylinder is also 7 cm.
The volume of the cylinder, $V_1=\pi r^2 h = \pi \left(\frac{7}{2}\right)^2 \times 7 = \frac{22}{7} \times \frac{49}{4} \times 7 =269.5\;\text{cm}^3$
The volume of the cube is $s^3$, where $s$ is the edge of the cube.
$V_2 = 7^3=343\;\text{cm}^3$
The volume of the cube left over after cutting the cylinder = $V_2 - V_1$ =  343 – 269.5 = 73.5 cm 3
Hence, the correct answer is 73.5.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books