Volume of a Cylinder Practice Quiz

The volume of a cylinder is determined by multiplying the area of its circular base (πr²) by its height (h). Therefore, the correct formula is V = πr²h.

By applying the formula V = πr²h, we calculate V = π(3²)(5) = π à - 9 à - 5, which equals 45π. Hence, 45π is the correct volume.

A right circular cylinder has a circular base, which is essential for using the formula V = πr²h. Other shapes do not apply for calculating the volume of a cylinder.

The volume formula V = πr²h requires only the radius and the height. The circumference is not necessary for this computation, making it the correct choice.

The area of a circle is given by A = πr², and this area is used in the cylinder volume formula. Therefore, πr² is the correct representation.

With a diameter of 8, the radius is 4. Using V = πr²h, we get V = π(4²)(10) = 160π. Thus, 160π is the correct volume.

Substitute the given values into the formula V = πr²h: 300π = πr² à - 10. Dividing both sides by 10π yields r² = 30, so r = √30, which is the correct answer.

Doubling the radius leads to (2r)² which equals 4r², so the volume becomes 4 times larger. Hence, the cylinder's volume quadruples when the radius is doubled.

Increasing the radius by a factor of 3 results in the area increasing by 3² = 9, and multiplying by the height (also increased by a factor of 3) gives an overall factor of 9 à - 3 = 27. Therefore, the volume increases 27 times.

Even though the can is open at the top, its volume is calculated using the full cylinder formula: V = πr²h = π(4²)(10) = 160π. This confirms the correct volume.

Both figures have their volume determined by multiplying the base area by the height. Since the base area and height are the same, the volumes are equal.

Since r = √a, squaring it gives r² = a. Substituting into the volume formula V = πr²h results in V = πa h, making it the correct representation.

Using V = base area à - height, we have 500 = 25π à - h, which gives h = 500/(25π) = 20/π. This is the height of the cylinder.

The constant π is used because the base of a cylinder is a circle, and π is essential in calculating areas and volumes related to circles. Therefore, π is the proper constant.

Since the height equals the diameter, we have h = 2r. Plugging this into V = πr²h yields V = πr²(2r) = 2πr³, which is the correct volume.

With the height defined as h = 2r, the volume becomes V = πr²(2r) = 2πr³. Setting 2πr³ equal to 128π leads to r³ = 64, and thus r = 4.

The new volume is V = π(3r)²(h/2) which simplifies to (9/2)πr²h. This shows the volume is multiplied by 9/2 compared to the original volume.

Since V = πr²h is constant, increasing the radius (and thus r²) requires the height to decrease in order to keep the product unchanged. Therefore, the height must decrease.

Reducing both the radius and height by 10% multiplies each by 0.9. The new volume becomes V = π(0.9r)²(0.9h) = 0.9³πr²h ≈ 0.729πr²h, which is roughly 72.9% of the original volume, or about 73%.

The cylinder's volume is normally given by V = πr²h. Given that r = x and V = 5πx², equate πx²h to 5πx², leading to h = 5. This is the correct height.