Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

General

General

Easy

Question

If a square card board piece of side 4 cm is rotated 360° about one of its sides, what is the volume of the solid so formed?

hint Hint:

A cylinder is a 3 dimensional figure with 2 circular bases, parallel to each other, which are joined by a curved surface.

Volume is the capacity of a certain object to carry or hold another objects within i.e. the amount of space that the object holds.

Volume of a cylinder = π r2 h

Circumference of a circle = 2 π r

π = 22/7

The correct answer is: Volume of the space covered by rotating a square piece of side 4 cm along its side will be 5.1 cm3.

Step-by-step solution:-
From the given information, we get- Side of the square = 4 cm.
Now, we know that a cylinder is made by rotating a sheet along its side to form a curved surface.

Hence, the object formed by rotating the given squarical cardboard piece is an open cylinder.
Now, From the adjacent diagram, we observe that-

side of the squarical piece will form the circumference of the base of the cylinder.

∴ Circumference of the base of the cylinder = Side of the square.
∴ Circumference of the base of the cylinder = 4
∴ 2π r = 4 ..................................... (Circumference of a circle = 2π r)
∴ 2 $cross times$ $22 over 7$ $cross times$ r = 4

∴ $44 over 7$ $cross times$ r = 4
∴ r = 4 $cross times$ $7 over 44$ ....................... (Dividing both sides by 44/7)

∴ r = $7 over 11$ cm ............................... (Equation i)
Now, we need to find the volume of the given object-
∴ Volume of the given object = Volume of a cylinder
∴ Volume of the given object = $pi r squared h$
∴ Volume of the given object = $22 over 7 space cross times space open parentheses 7 over 11 close parentheses squared cross times space 4$ .......................................... (From Equation i)
∴ Volume of the given object ≈ 5.1 $c m cubed$ .

∴ Volume of the space covered by rotating a square piece of side 4 cm along its side will be 5.1 $c m cubed$ .

Related Questions to study

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.