Volume of cylinders

Front

What is the formula for the volume of a cylinder?

Back

Volume = πr²h, where r is the radius and h is the height.

Front

What does 'π' represent in the volume formula?

Back

π (pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

How do you find the radius of a cylinder if you know the diameter?

Back

Radius = Diameter / 2.

Front

If a cylinder has a height of 10 cm and a radius of 3 cm, what is its volume?

Back

Volume = π(3 cm)²(10 cm) = 90π cm³ ≈ 282.74 cm³.

Front

What is the volume of a cylinder with a radius of 4 inches and a height of 5 inches?

Back

Volume = π(4 in)²(5 in) = 80π in³ ≈ 251.33 in³.

Front

What units are used to measure the volume of a cylinder?

Back

Cubic units, such as cm³, m³, in³, or ft³.

Front

What is the relationship between the volume of a cylinder and its height?

Back

The volume of a cylinder increases linearly with height; if height doubles, volume doubles.

Front

If the radius of a cylinder is tripled, how does the volume change?

Back

The volume increases by a factor of 9, since volume is proportional to the square of the radius (V ∝ r²).

Front

What is the volume of a cylinder with a diameter of 6 m and a height of 10 m?

Back

First, find the radius: r = 6 m / 2 = 3 m. Then, Volume = π(3 m)²(10 m) = 90π m³ ≈ 282.74 m³.

Front

How can you determine if a certain volume of liquid will fit in a cylindrical container?

Back

Calculate the volume of the cylinder using the formula and compare it to the volume of the liquid.