Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
5.6k views
in Surface Area and Volume by (49.4k points)
closed by

Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm. (π = 22/7)

1 Answer

+1 vote
by (48.7k points)
selected by
 
Best answer

Given: Radius (r) = 28 cm, 

Total surface area of cone = 7128 sq.cm 

To find: Volume of the cone 

i. Total surface area of cone = πr (l + r) 

∴ 7128= y x 28 x (l + 28) 

∴ 7128 = 22 x 4 x(l +28) 

∴ l + 28 = 7128/22 x 4

∴ l + 28 = 81 

∴ l = 81 – 28 

∴ l = 53 cm

ii. Now, l2 = r2 + h2 

∴ 532 = 282 + h2 

∴ 2809 = 784 + h2 

∴ 2809 – 784 = h2

∴ h2 = 2025

∴ h = √2025 … [Taking square root on both sides] 

= 45 cm

= 22 x 4 x 28 x 15 

= 36960 cm3 

∴ The volume of the cone is 36960 cm3.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...