Question

A rectangular sheet of dimensions 44cm x 7cm is rotated about its longer side find the volume and the total surface area of the solid thus generated.

Answer 1

Answer:

Step-by-step explanation:

volume= 1078cm^3

surface area = 616cm^2

Answer 2

Volume of the cylinder thus generated is 1078 cm³.

Surface area of the cylinder 308 cm².

Given:

• A rectangular sheet of 44cm × 7 cm.
• It is rotated about its longer side.

To find:

• Find the volume and total surface area of solid so formed.

Solution:

Formula/Concept to be used:

• When a rectangular sheet is folded/rotated a right circular cylinder is formed; which is like a pipe, i.e. both ends are open.

• Volume of cylinder $V_c = \pi \: {r}^{2} \: h$

• Curved Surface area of the cylinder $S_c=2\pi \: rh$

Step 1:

Find the dimension of the cylinder.

The circumference of the base of the cylinder (Length of rectangular sheet)= 44 cm

$2\pi \: r = 44$

$\implies \: r = \frac{44 \times 7}{2 \times 22}$

$\implies \: \bf r = 7 \: cm$

Height of the cylinder (h)(Breadth of rectangular sheet)= 7 cm

Step 2:

Find the volume of the cylinder.

$\bf V_c= \pi \: {r}^{2} h$

$\implies \: V_c = \frac{22}{7} \times 7 \times 7 \times 7$

$\implies \: V_c= 22 \times 49$

$\implies \: \bf V_c= 1078 \: {cm}^{3}$

Thus,

The volume of the cylinder is 1078 cm³.

Step 3:

Find the surface area of the cylinder.

As,

The cylinder so formed is hollow; i.e. open from base and top.

Surface area

$\bf S_c = 2\pi \: rh$

$\implies \: S_c = 2 \times \frac{22}{7} \times 7 \times 7$

$\implies \: S_c = 22 \times 14$

$\implies \: \bf S = 308 \: {cm}^{2}$

So,

Surface area of the cylinder is 308 cm².

Thus,

The volume of the cylinder is 1078 cm³.

Surface area of the cylinder 308 cm².

Learn more:

1) The volume of a cylinder of height 28 cm is 4312 cm . Find the surface area of the cylinder

https://brainly.in/question/49034563

2)A right circular solid cylinder has radius 7cm and height 24cm. A conical cavity of same dimensions is carved out of the...

https://brainly.in/question/7517135

#SPJ3