Question

a volume of cylinder 924 cm³ and curved surface area is 264 cm²then height is.....
a)4 m
b)5 m
c)6cm
d)7 m
please find step by step......​

Answer 1

Recall:

$\text{Volume of a cylinder = }\pi r^2h$

$\text{Curved Surface Area }= 2\pi rh$

Make h the subject:

$\text{Volume of a cylinder = }\pi r^2h$

$\text{Volume of a cylinder = } 924 \text{cm}^3$

$\pi r^2h = 924$

$h = \dfrac{924}{\pi r^2}$

Make h the subject:

$\text{Curved Surface Area }= 2\pi rh$

$\text{Curved Surface Area }= 264 \text{ cm}^2$

$2\pi rh = 264$

$h = \dfrac{132}{\pi r}$

Solve r:

$h = \dfrac{924}{\pi r^2}$

$h = \dfrac{132}{\pi r}$

$\dfrac{132}{\pi r} = \dfrac{924}{\pi r^2}$

$132r = 924$

$r = 7$

Find the height:

$h = \dfrac{132}{\pi r}$

$h = \dfrac{132}{\pi (7)}$

$h = 6 \text{ cm}$

Answer: (c) 6 cm

Answer 2

Step-by-step explanation:

of a cylinder = πr

2

h

\text{Curved Surface Area }= 2\pi rhCurved Surface Area =2πrh

Make h the subject:

\text{Volume of a cylinder = }\pi r^2hVolume of a cylinder = πr

2

h

\text{Volume of a cylinder = } 924 \text{cm}^3Volume of a cylinder = 924cm

3

\pi r^2h = 924πr

2

h=924

h = \dfrac{924}{\pi r^2}h=

πr

2

924

Make h the subject:

\text{Curved Surface Area }= 2\pi rhCurved Surface Area =2πrh

\text{Curved Surface Area }= 264 \text{ cm}^2Curved Surface Area =264 cm

2

2\pi rh = 2642πrh=264

h = \dfrac{132}{\pi r}h=

πr

132

Solve r:

h = \dfrac{924}{\pi r^2}h=

πr

2

924

h = \dfrac{132}{\pi r}h=

πr

132

\dfrac{132}{\pi r} = \dfrac{924}{\pi r^2}

πr

132

=

πr

2

924

132r = 924132r=924

r = 7r=7

Find the height:

h = \dfrac{132}{\pi r}h=

πr

132

h = \dfrac{132}{\pi (7)}h=

π(7)

132

h = 6 \text{ cm}h=6 cm