Question

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

Answer 1

Answer:

volume=1078 cm^3

total surface area=616 cm^3

Step-by-step explanation:

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Answer 2

Volume of cylinder is 1078 cm³.

Surface area of 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:

• Right circular cylinder is formed,when rectangular sheet is folded.
• Volume of cylinder$V = \pi \: {r}^{2} \: h$
• Curved Surface area of the cylinder $S=2\pi \: rh$

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 volume of cylinder.

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

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

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

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

Thus,

Volume of cylinder is 1078 cm³.

Step 3:

Find surface area of cylinder.

As,

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

Surface area

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

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

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

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

So,

Surface area of the cylinder 308 cm².

Thus,

Volume of cylinder is 1078 cm³.

Surface area of cylinder 308 cm².

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