Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is $4838.4 \pi ~\mathrm{cm}^3$, then its radius is:
Option 1: 28 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 24 cm
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 24 cm
Solution : The ratio of slant height and radius = 29 : 20 Let slant height($l$) be $29x$ and radius($r$) be $20x$. Height, $h = \sqrt{l^2-r^2} = \sqrt{(29x)^2-(20x)^2} = \sqrt{(841-400)x^2}= \sqrt{441x^2} = 21x$ Volume of cone = $4838.4 \pi$ ⇒ $\frac{1}{3} \pi r^2 h = 4838.4 \pi$ ⇒ $\frac{1}{3}× \pi ×(20x)^2 × 21x = 4838.4 \pi$ ⇒ $x^3 = \frac{4838.4×3}{400×21} = \frac{172.8}{100}=1.728$ ⇒ $x=\sqrt[3]{1.728}=1.2$ Radius = $20x = 20 × 1.2 = 24$ cm Hence, the correct answer is 24 cm.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : The ratio of the height and the diameter of a right circular cone is 6: 5 and its volume is $\frac{2200}{7} \mathrm{~cm}^3$. What is its slant height? (Take $\pi=\frac{22}{7}$ )
Question : The volume of a cone with a height equal to the radius and slant height of 5 cm is:
Question : The radius of a solid right circular cone is 36 cm and its height is 105 cm. The total surface area (in cm2) of the cone is:
Question : A right circular cone is 3.6 cm high, and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone with a radius of 1.2 cm at its base. Then the height of the cone (in cm) is:
Question : The curved surface area of a right circular cone of a base radius of 21 cm is 594 sq. cm. What is the slant height of the cone?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile