Question
Find the volume of the space covered by rotating a rectangular sheet of dimensions 16.1 cm × 7.5 cm along its length.
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 =
- Circumference of a circle = 2 π r
- π =
The correct answer is: ∴ Volume of the space covered by rotating a rectangular sheet of dimensions 16.1 cm × 7.5 cm along its length will be 154.64 cm3.
Step-by-step solution:
From the given information, we get-
- Length of the rectangular sheet = 16.1 cm
- Width of the rectangular sheet = 7.5 cm
Now, we know that a cylinder is made by rotating a rectangular sheet along its length to form a curved surface.
Hence, the object formed by rotating the given rectangular sheet is an open cylinder.
Now, From the adjacent diagram, we observe that-
Length of the rectangular sheet will form the circumference of the base of the cylinder.
∴ Circumference of the base of the cylinder = length of the rectangle.
∴ Circumference of the base of the cylinder = 16.1
∴ 2π r = 16.1 ..................................... (Circumference of a circle = 2π r)
∴ 
= 16.1
∴ 
r = 16.1
∴ r = 16.1 
....................... (Dividing both sides by 44/7)
∴ r ≈ 2.56 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 =
∴ Volume of the given object = 
.......................................... (From Equation i)
∴ Volume of the given object ≈ 154.64 
.
∴ Volume of the space covered by rotating a rectangular sheet of dimensions 16.1 cm × 7.5 cm along its length will be 154.64 .
Now, From the adjacent diagram, we observe that-
Length of the rectangular sheet will form the circumference of the base of the cylinder.
∴ Circumference of the base of the cylinder = length of the rectangle.
∴ Circumference of the base of the cylinder = 16.1
∴ 2π r = 16.1 ..................................... (Circumference of a circle = 2π r)
∴
= 16.1∴
r = 16.1∴ r = 16.1
....................... (Dividing both sides by 44/7)∴ r ≈ 2.56 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 =
∴ Volume of the given object =
.......................................... (From Equation i)∴ Volume of the given object ≈ 154.64
.∴ Volume of the space covered by rotating a rectangular sheet of dimensions 16.1 cm × 7.5 cm along its length will be 154.64
.
