The total surface area of a …

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

The total surface area of a cylinder is 462cm².Its curved surface area is one third of its total surface area.Find the volume of the cylinder.

Posted by Modi Srivastava 3 years, 8 months ago

CBSE > Class 09 > Mathematics

3 answers

Lakshya Shrivastava 3 years, 8 months ago

find a&b , if 2-√5 =a√5 + b 2+3√5

0Thank You

Khushi Kaur 3 years, 8 months ago

Let r cm be the radius of the base and h cm be the height of the cylinder, Then, total surface area of cylinder = 2πr (r + h) Curved surface area of cylinder = 2πrh We have, Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm2 = 154 cm2 ⇒ 2πrh = 154 Also, 2πrh + 2πr2 = 462 ⇒ 154 + 2πr2 = 462 ⇒ 2πr2 = 462 - 154 = 308 cm2 2 x 22/7 x r2 = 308 ⇒ r2 = 308 x 7/2 x 22 = 72 ⇒ r = 7 cm Again 2πrh = 154 ⇒ 2 x 22/7 x 7 x h = 154 ⇒ h = 154/2 x 22 = 7/2 cm Volume of the cylinder = πr2h = 22/7 x 7 x 7 x 7/2 = 539 cm3

1Thank You

Palak Gupta 3 years, 8 months ago

Given, total surface area of cylinder = 462 square cm. Also, CSA of cylinder = 3 TSA of ccylinder ⇒TSA=2πrh+2πr2 ⇒TSA=CSA+2πr 2 ⇒TSA= 3TSA +2πr 2 ⇒ 32TSA =2πr 2 ⇒ 3TSA =πr2 ⇒ 3462 = 722 ×r 2 ⇒r=7cm Now, CSA of cylinder = 3 TSA of ccylinde = 3462 =154cm 2 ⇒2πrh=154 ⇒2× 7 22 ×7×h=154 ⇒h= 27cm Therefore, volume of the cylinder =πr 2 h= 722 ×7 2 × 27 =539cm 3 Hence, volume of the solid cylinder is 539cm 3 .

2Thank You

ANSWER