Question

The voluine and height of a cylinder are 38.5 cm^3
and 4 cm respectively. Find the curved surface
area and total surface area of the cylinder.​

Answer 1

volume of CYLINDER = PIE Ŕ²H

22/7 × R²×4 = 38.5 CM³

SOLVE THIS U WILL GET R

THAT IS RADIUS

NOW FOR CURVED SURFACE USE (2(PIE) RH )

AND FOR TOTAL SURFACE USE (2 PIE R) ( R +H )

PIE = 22/7 APPROXIMATELY

Answer 2

Answer

Curved surface area = 44 cm

Total surface area = 63.25 m^ 2

Some important formula of right circular cylinder .

$(1)curved \: surface \: area \: of \: cylinder = 2\pi \: rh$

$(2)total \: surface \: area \: of \: cylinder \: = 2 \: \pi \: r \: (h + r)$

$(3)volume \: of \: cylinder \: = \pi \: {r}^{2} h$

Formula used

$\: \: \: \: .volume \: of \: cylinder \: = \pi {r}^{2} h$

$\: \: \: \: . \: \: curved \: surface \: area \: = 2\pi \: rh$

$\: \: \: \: . \: \: total \: surface \: area \: = 2\pi \: r(h + r)$

Solution

Given

Volume of the cylinder = 38.5 cm ^ 3

Height = 4 cm

To find

(1) curved surface area ?

(2) Total surface area ?

Solution

We know that

Volume = 38.5 cm^ 3

Height = 4 cm

According to the question

$= = > \pi {r}^{2} h \: = 38.5 {cm}^{3}$

$= = > \frac{22}{7} \times {r}^{2} \times 4 = 38.5 \\ = = > {r }^{2} = \frac{38.5 \times 7}{22 \times 4} = 3.0625$

$= = > {r}^{2} = 3.0625 \\ = = > r = 1.75$

$to \: find \: curved \: surface \: area \: = 2\pi \: rh$

$= = > 2 \times \frac{22}{7} \times 1.75 \times 4 = 44$

Hence curved surface area = 44 cm

$to \: find \: total \: surface \: area \: = 2\pi \: r(h + r)$

$= = > 2 \times \frac{22}{7} \times 1.75(4 + 1.75)$

$= = > 2 \times \frac{22}{7} \times 1.75 \times 5.75 = 63.25$

Hence your total surface area = 63.25cm ^2

Hope it is helpful for you