The area of a curved surface of a right circular cylinder is 100 sq, cm. and its volume is 150 cubic cm. Find the height and the radius of the cylinder.

Shohan

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2025-01-04 04:42

1 Answers

Shohan

$L e t, t h e r a d i u s a n d h e i g h t o f t h e c y l i n d e r b e r a n d h c m r e s p e c t i v e l y . W e k n o w, s u r f a c e a r e a o f c y l i n d e r i s = 2 πrh {cm}^{2}$

$A n d v o l u m e o f t h e c y l i n d e r i s = {πr}^{2} h {cm}^{3} According to question, 2 πrh = 100 . . . . . . . . . (i) And, {πr}^{2} h = 150 . . . . . . . (ii) Dividing equation (ii) by equation (i), we get$

$\frac{{πr}^{2} h}{2 πrh} = \frac{150}{100} = \frac{r}{2} = \frac{3}{2} ∴ r = 3 c m P u t t i n g, r = 3 i n e q u a t i o n (i), w e g e t 2 πrh = 100 ∴ h = \frac{100}{2 πr} = \frac{100}{2 \times 3 \times 3.1416} = 5.3 cm ∴ Required radius = 3 cm and height = 5.3 cm .$

4 views Answered 2024-12-14 13:31

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