Question

radius of the wheel shown below is 7 cm. how many rotations are needed for this wheel to cover 440 cm​

Answer 1

Answer :

Number of rotations of the wheel is 10 rotations

Step-by-step explanation :

To Find,

• Number of rotations ...... ( ? )

Given that,

• Radius of the wheel is 7 cm
• Rotations required for the wheel to cover 440 cm

Solution,

First let's find the circumference, as

1 rotation = Circumference

Circumference = 2πr

∴ Circumference of the wheel is

= 2 × 22/7 × 7

Dividing 7 and 7 with 7

= 2 × 22

= 44cm

∴ Circumference of the wheel is 44 cm

Now, let's find, number of rotations required for the wheel to cover 440 cm

We know that,

Number of rotations = Total distance travelled / Circumference

∴ Number of rotations

= 440 / 44

Dividing 440 and 44 with 4

= 40 / 4

Dividing 40 and 4 with 4

= 10

∴ Number of rotations required for the wheel to cover 440 cm is 10.

Answer 2

$\large \sf \underline{ \underline{ \red{given : }}}$

• Radius of wheel = 7cm.
• Distance covered = 440cm.

$\\ \\ \large \sf \underline{ \underline{ \red{to \: find : }}}$

• Number of rotations needed to cover 440cm.

$\\ \\ \large \sf \underline{ \underline{ \red{to \: know : }}}$

$\boxed{ \pink{circumference = 2\pi \: r}}$

Here ,

• π = 22/7

• r = 7cm

$\\ \\ \large \sf \underline{ \underline{ \red{solution : }}}$

➤ With one rotation, it will cover the circumference of the wheel.

Circumference = 2πr

$\\ \implies \sf{2( \frac{22}{ \cancel7} )( \cancel7)} \\ \\ \implies \sf{44 cm }$

➤ So, with one rotation, wheel will cover 44cm.

➤ We have to find , how many rotations will it take to cover 440cm.

So,

$\sf{no. \: of \: rotations \: = \frac{total \: distance}{distance \: covered \: in \: one \: rotation} } \\ \\ \sf{no. \: of \: rotations \: = \frac{440 cm }{44cm} } \\ \\ \boxed{ \red{\sf{no. \: of \: rotations = 10}}}$

$\therefore \: \rm \: \blue{ 10 \: rotations }\: are \: required \: to \: cover \: \\ \: \: \: \: \: \: \rm{440cm.}$