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

Maths-

General

Easy

Question

The radius of the base of a right circular cylinder is doubled and the height is halved. What is the ratio of volume of the new cylinder to that of the original cylinder?

hint Hint:

We simply recall the formulae and find the ratio.

The correct answer is: The required ratio is 2 : 1.

Explanations:
Step 1 of 2:
Let the radius of the base of a right circular cylinder be r and height be h.
Volume of the cylinder, $V subscript text original end text end subscript equals pi r squared h$
The radius of the base of a right circular cylinder is doubled and the height is halved.
So, radius of new cylinder = $2 r$
Height of new cylinder = $equals h over 2$
Volume of the new cylinder, $V subscript text new end text end subscript equals pi left parenthesis 2 r right parenthesis squared open parentheses h over 2 close parentheses equals 2 pi r squared h$
Step 2 of 2:
So, ratio of volume of new cylinder to the original cylinder,
$V subscript text new end text end subscript over V subscript text original end text end subscript equals fraction numerator 2 pi r squared h over denominator pi r squared h end fraction equals 2$
Final Answer:
The required ratio is 2 : 1.

Related Questions to study

Two sides of a parallelogram are 7 inch and 4 inch respectively. The angle between them is 30 degrees. Find its area

Two sides of a parallelogram are 7 inch and 4 inch respectively. The angle between them is 30 degrees. Find its area

Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

A Cylinder and cone are of the same height. If diameter of their bases are in the ratio 2:3, Find the ratio of their volumes?

A Cylinder and cone are of the same height. If diameter of their bases are in the ratio 2:3, Find the ratio of their volumes?

parallel

During Van Mahotsav, some children planted trees in a triangular region, two sides of which are 18 m and 10 m and the perimeter is 42 m. Find the area of the planted region.

During Van Mahotsav, some children planted trees in a triangular region, two sides of which are 18 m and 10 m and the perimeter is 42 m. Find the area of the planted region.

If the area of a parallelogram is 300m² and the base of the parallelogram is thrice its height, find the base and height of a parallelogram.

If the area of a parallelogram is 300m² and the base of the parallelogram is thrice its height, find the base and height of a parallelogram.

Identify the equation of a line parallel to the line y = x – 1

Identify the equation of a line parallel to the line y = x – 1

parallel

Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.

Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.

What is the area of a parallelogram with coordinated , $left parenthesis 0 comma 0 right parenthesis comma left parenthesis 1 comma 4 right parenthesis comma left parenthesis 3 comma 4 right parenthesis comma text and end text left parenthesis 2 comma 0 right parenthesis ?$

What is the area of a parallelogram with coordinated , $left parenthesis 0 comma 0 right parenthesis comma left parenthesis 1 comma 4 right parenthesis comma left parenthesis 3 comma 4 right parenthesis comma text and end text left parenthesis 2 comma 0 right parenthesis ?$

Identify the equation of a line perpendicular to the line x/2 + y = -1

Identify the equation of a line perpendicular to the line x/2 + y = -1

parallel

If the area of an equilateral triangle is 16 $square root of 3$ cm² find the length of the side of the triangle.

If the area of an equilateral triangle is 16 $square root of 3$ cm² find the length of the side of the triangle.

Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.

A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.

parallel

Identify the line having y-intercept = $1 half$

Identify the line having y-intercept = $1 half$

Find the perimeter and height of an equilateral triangle whose area is equal to 60 $square root of 3$ cm²

Find the perimeter and height of an equilateral triangle whose area is equal to 60 $square root of 3$ cm²

A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.

A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.

parallel

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.