Question

11 12 if a cylinders height is halved and its radius remains the same, what happens to its volume? a. it stays the same. b. it triples. c. it doubles. d. it halves. the area of the base of a cylinder can be calculated using which of the following formulas? a. $a = 2\pi rh$ b. $a = \pi r^2$ c. $a = l \times w$ d. $a = \frac{1}{2}bh$ a cylinder has a radius of 7 cm and a volume of $539\pi \text{cm}^3$. what is its height? a. 11 cm b. 12 cm c. 13 cm d. 14 cm if a cylindrical water tank has a radius of 6 meters and a height of 10 meters, what is its volume? a. 452.16 cubic meters b. 376.99 cubic meters c. 314.16 cubic meters d. 1351.04 cubic meters which of the following real - world objects is an example of a cylinder? a. a book b. a can of soda c. a sphere d. a pyramid which of the following formulas can be used to calculate the volume of a cylinder? a. $v = \frac{1}{3}\pi r^2h$ b. $v = \frac{4}{3}\pi r^3$ c. $v = \pi r^2h$ d. $v = 2\pi rh$

Explanation:

Step1: Recall cylinder volume formula

The volume of a cylinder is $V = \pi r^2 h$, where $r$ = radius, $h$ = height.
---

Question 1

Step1: Substitute new height into formula

New height: $h' = \frac{h}{2}$. New volume: $V' = \pi r^2 \cdot \frac{h}{2}$

Step2: Compare to original volume

$V' = \frac{1}{2} \pi r^2 h = \frac{1}{2}V$
---

Question 2

Step1: Identify base shape of cylinder

The base of a cylinder is a circle; area of a circle is $A = \pi r^2$.
---

Question 3

Step1: Rearrange volume formula for height

$h = \frac{V}{\pi r^2}$

Step2: Substitute given values

$V=539\pi$, $r=7$. $h = \frac{539\pi}{\pi (7)^2} = \frac{539}{49}$

Step3: Calculate the value

$\frac{539}{49} = 11$
---

Question 4

Step1: Substitute values into volume formula

$r=6$, $h=10$. $V = \pi (6)^2 (10) = 360\pi$

Step2: Compute numerical value

$360 \times 3.1416 = 1130.976 \approx 1131.04$
---

Question 5

Step1: Match object to cylinder shape

A cylinder has two circular parallel bases and a curved lateral surface; a soda can fits this.
---

Question 6

Step1: Recall cylinder volume formula

Volume of a cylinder is base area (circle) times height: $V = \pi r^2 h$

Answer:

1. d. It halves.
2. b. $A = \pi r^2$
3. a. 11 cm
4. d. 1131.04 cubic meters
5. b. A can of soda
6. c. $V = \pi r^2 h$