7 Views

Question : The radius and height of a right circular cone are in the ratio 1 : 2.4. If its curved surface area is 2502.5 cm2, then what is its volume? (Take $\pi=\frac{22}{7}$)

Option 1: 8085 cm3

Option 2: 8820 cm3

Option 3: 11550 cm3

Option 4: 13475 cm3


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 13475 cm 3


Solution : The ratio of the radius and height of a right circular cone = 1 :  2.4 = 10 : 24 = 5 : 12
Let radius, $r = 5x$, height, $h=12x$ and slant height be $l$.
$l^2 = r^2 + h^2 = (5x)^2 + (12x)^2 = 25x + 144x = 169x^2$
⇒ $l = \sqrt{169x^2}=13x$
Curved surface area of a cone = $\pi r l$
⇒ $2502.5 = \frac{22}{7} × 5x × 13x$
⇒ $x^2 = \frac{2502.5 × 7}{22 × 5 × 13} = 12.25$
⇒ $x = 3.5$
Now, the volume of a cone = $\frac{1}{3}\pi r^2h$
= $\frac{1}{3}×\frac{22}{7}×(5x)^2×12x$
= $\frac{1}{3}×\frac{22}{7}×25× 3.5^2 ×12×3.5$
= 13475 cm 3
Hence, the correct answer is 13475 cm 3 .

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