Can two cylinders have the same volume but different dimensions?
No. The height of the oblique cylinder will be less than its slant height of 4 inches. Because the overall height of the two cylinders is not the same, the volumes will be different.
Can two cylinders with the same volume have different surface areas?
The short answer is “No”. For a given volume, the surface area of a cylinder can be as large or as small as you like.
How does changing dimensions affect volume?
When the dimensions of the shape, such as radius, height, or length change, both surface area and volume also change. However, the volume of the object always changes more than the surface area for the same change in dimensions.
Do the cylinders have the same volume?
Do they have the same volume? Yes, due to Cavalieri’s principle. Even though these two cylinders are different, because they have the same height and base (and because every parallel cross section is congruent to the base), their volumes will be the same.
Does a cylinder and a rectangular prism with the same height have the same volume?
A cylinder and a rectangular prism have the same volume and same height. The base of the prism is a square with side length 7 cm.
What are the two different cylinders?
Types of Cylinder Right Circular Cylinder: If the axis of the two parallel bases is perpendicular to the center of the base, it is called the right circular cylinder. Oblique Cylinder: An oblique cylinder is one whose sides lean over the base. In this, the sides are not perpendicular to the center of the base.
How does volume and surface area relate to 2 dimensional area?
There is no definite relation between area and volume, as area is two dimensional and volume is 3 dimensional.
How would you explain the difference between surface area and volume of three-dimensional shapes?
Surface area and volume are different attributes of three-dimensional figures. Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas.
How is the volume of the cylinder affected if the height of the cylinder is multiplied by 3 and the radius is multiplied by 2?
Given this orientation, and as observed by another answer, tripling the radius, which then gets squared in the volume formula, will increase the volume by a factor of 3^2 or 9. Volume of cylinder is proportional to the square of radius of the cylinder. If radius is tripled then volume becomes 9 times.
What is the difference between dimension and volume?
As nouns the difference between volume and dimension is that volume is a unit of three-dimensional measure of space that comprises a length, a width and a height it is measured in units of cubic centimeters in metric, cubic inches or cubic feet in english measurement while dimension is dimension.
Why the volume formula is the same for both a prism and for a cylinder?
The cylinder and the prism have the same cross-sectional area, πr2, at every level and the same height. By Cavalieri’s Principle, the prism and the cylinder have the same volume. where B is the area of a base, h is the height, and r is the radius of a base.
What is similar and what is different between the formulas for volume for a rectangular prism a triangular prism and a cylinder?
They are both similar in the way that the formula is base multiplied by height. They are different becasue of the type of shape on the base.