Question

A hollow cylinder of height 21 cm and volume 7276.5 cm³ circumscribes a cone having the same base as the cylinder. The CSA of the cone is half of the CSA of the cylinder. Find the height of the cone.
1. 16
2. 17
3. 18
4. 19

Answer 1

Correct Answer - Option 3 : 18

GIVEN:

Height of hollow cylinder = 21cm

Volume of hollow cylinder = 7276.5 cm3 

CSA of the cone = 1/2 × CSA of the cylinder

 

FORMULAS USED:

Volume of cylinder = \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdahaaa!37B0! π \)π r²h

CSA of cylinder = 2π rh

CSAof cone = π rl

 

EXPLANATION:

Volume of cylinder \(\pi\)r²h = 7276.5

\(\frac{22}{7}\times r^2\times21 = 7276.5\)

\(r^2 = \frac{7276.5}{66} = 110.25\)

r = 10.5

Since the base of cone and cylinder is same the radius of the cone is also 10.5

now, CSA of cone = \(\frac12\)CSA of cylinder

\(\therefore π rl = \frac122π rh\) \(\rightarrow\) l = h

l = 21

now, height of cone h² = l² - r²

h² = 21² - 10.5² 

h = 18