Question

The volume of a cylindrical soap dispenser is modeled by the expression below.

pi(x+1)^2(4x+1)

Select the true statement. A. The factor 4x + 1 represents the height of the soap dispenser. B. The factor 4x + 1 represents the area of the base of the soap dispenser. C. The expression (x + 1)2 represents the height of the soap dispenser. D. The expression (x + 1)2 represents the radius of the soap dispenser.

Answer 1

answer : option (A), The factor (4x + 1) represents the height of soap dispenser.

explanation : standard form of volume of cylinder is given as, V = πr²h ......(1)

• V is volume of volume of cylinder.
• where r is radius of base of cylinder
• h is height of cylinder.

a/c to question, volume of cylinderical soap dispenser, V = π(x + 1)² (4x + 1) .....(2)

on comparing equations (1) and (2),

we get, r² = (x + 1)² and h = (4x + 1)

hence, (x + 1)² represents square of radius of soap dispenser and (4x + 1) represents height of soap dispenser.

hence, option (A) is correct choice.

Answer 2

Answer:

Option A is correct

A. The factor 4x + 1 represents the height of the soap dispenser.

Step by step Explanation:

We know that volume of right circular cylinder is

$\boxed{V_{cylinder}=\pi\:r^2\:h}$

where r is radius of Cylinder and

h is height of Cylinder

So now to compare this expression to the volume of cylindrical soap dispenser

$V_{soap\:dispenser}=\pi\:(x+1)^2\:(4x+1)$

it is clear here that radius of

cylindrical soap dispenser is:(x+1)

it's height is (4x+1)

Thus out of the given options option A is correct.