6 Views

Question : From a solid right circular cylinder of length 4 cm and diameter 6 cm, a conical cavity of the same height and base is hollowed out. The whole surface of the remaining solid (in square cm) is:

Option 1: 48$\pi$

Option 2: 15$\pi$

Option 3: 63$\pi$

Option 4: 24$\pi$


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 7th Jan, 2024

Correct Answer: 48$\pi$


Solution : Given: Diameter = 6 cm
So, radius, $r$ = $\frac{6}{2}$ = 3 cm
Height, $h$ = 4 cm
$\therefore$ Curved surface area of the cylinder $=2\pi rh=2\pi×3×4=24\pi$
Now, slant height, $l$ = $\sqrt{r^2+h^2}$ = $\sqrt{3^2+4^2}$ = $5$
So, the curved surface area of the cone $=\pi rl=\pi×3×5=15\pi$
Area of the circle on the top $=\pi r^2=\pi×3^2=9\pi$
Required whole surface area
= curved surface area of cylinder + curved surface area of cone + area of the circle
= $24\pi+15\pi+9\pi$
= $48\pi$
Hence, the correct answer is 48$\pi$.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

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