1 View

Question : A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be:

Option 1: $1 : 2$

Option 2: $2 : 1$

Option 3: $1:\sqrt{2}$

Option 4: $\sqrt{2}:1$


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 13th Jan, 2024

Correct Answer: $\sqrt{2}:1$


Solution : Since the bases of the hemisphere and cone are equal, their radii are also equal.
⇒ radius of hemisphere = radius of cone = $r$
Height of hemisphere = radius of hemisphere = $r$
Also, height of cone = height of hemisphere = $r$
The slant height of the cone, $l$ = $\sqrt{r^{2}+r^{2}} = \sqrt{2}r$
Curved surface area of a hemisphere $= 2\pi r^{2}$
The curved surface area of a cone $= \pi rl$
Require ratio $= 2\pi r^{2}:\pi rl$
$= 2\pi r^{2}:\pi r\sqrt{2}r$
$= \sqrt{2}:1$
Hence, the correct answer is $\sqrt{2}:1$.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

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