Question

The curved surface area of a cylinder is 880cm2 and its volume is 770cm3.Find its diameter and height.

Answer 1

Answer:

The height of cylinder is: h = 80.07 cm

The diameter of cylinder is: d = 3.5 cm

Step-by-step explanation:

Curved surface area of cylinder = 880 cm^2

Volume of cylinder = 770 cm^3

We need to find its diameter and height.

The formula used are:

$Curved\: surface\: area=2\pi rh\\Volume=\pi r^2h$

If we divide volume by curved surface, we can find radius

$\frac{Volume}{Curved\: surface\: area}=\frac{\pi r^2h}{2\pi rh} \\\frac{770}{880}=\frac{r}{2}\\0.875= \frac{r}{2}\\=> r= 0.875\times 2\\r=1.75$

So, we get radius r = 1.75

Now, we can find height using curve surface area formula:

$Curved\: surface\: area=2\pi rh\\880=2(3.14)(1.75)h\\h=\frac{880}{10.99}\\h=80.07 \:cm$

So, the height of cylinder is: h=80.07 cm

Now finding diameter using formula: $d=2r$

Putting value of r in above formula:

$d=2r\\d=2(1.75)\\d=3.5\:cm$

So, the diameter of cylinder is: d = 3.5 cm