Question : A solid cone of height 42 cm with a diameter of its base of 42 cm is cut out from a wooden solid sphere of radius 24 cm. Find the percentage of wood wasted correct to two places of decimal.
Option 1: 75.56%
Option 2: 56.65%
Option 3: 66.50%
Option 4: 67.50%
Latest: SSC CGL 2024 final Result Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: 66.50%
Solution : Given, the height of the cone, $h_c$ = 42 cm Radius of cone, $r_c$ = $\frac{42}{2}$ cm = 21 cm Radius of sphere, $r_s$ = 24 cm Volume of sphere = $\frac{4}{3} \pi r_s^3$ = $\frac{4}{3} \pi \times{24}^3$ = $18432\pi$ cm3 Volume of cone = $ \frac{\pi r_c^2 h_c}{3}$ = $ \frac{\pi\times 21^2\times 42}{3}$ = $6174\pi$ cm3 Wood wasted = Volume of Sphere – Volume of cone = $18432\pi-6174\pi$ = $12258\pi$ cm3 Percentage of wood wasted = $ \frac{\text{Volume of Sphere – Volume of cone}}{\text{Volume of Sphere}}\times 100$ = $\frac{12258\pi}{18432\pi}\times 100$ = 66.50% Hence, the correct answer is 66.50%.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : A solid metallic sphere of radius 12 cm is melted and recast into a cone having a diameter of the base of 12 cm. What is the height of the cone?
Option 1: 258 cm
Option 2: 192 cm
Option 3: 166 cm
Option 4: 224 cm
Question : A solid metallic sphere of radius 13 cm is melted and recast into a cone having a diameter of the base as 13 cm. What is the height of the cone?
Option 1: 246 cm
Option 2: 152 cm
Option 3: 174 cm
Option 4: 208 cm
Question : A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percentage of the material is wasted in this process?
Option 1: 25
Option 2: 0
Option 3: 5
Option 4: 10
Question : The radius of the base of a hollow cone is 8 cm, and its height is 15 cm. A sphere of the largest radius is put inside the cone. What is the ratio of the radius of the base of a cone to the radius of a sphere?
Option 1: 5 : 3
Option 2: 4 : 1
Option 3: 2 : 1
Option 4: 7 : 3
Question : The volume of a cone is 73920 cm3. If the height of the cone is 160 cm, find the diameter of its base.
Option 1: 21 cm
Option 2: 40 cm
Option 3: 22 cm
Option 4: 42 cm
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile