if the height of the cylinders is 18 units, which expression is equivalent to the volume of the shaded part of the figure in cubic units?

$\pi(5-2)^2(18)$
$\pi(18)^2(5)-\pi(18)^2(2)$
$\pi(5)^2(18)-\pi(2)^2(18)$
$\pi(18)^2(5-2)$

Question

if the height of the cylinders is 18 units, which expression is equivalent to the volume of the shaded part of the figure in cubic units?

$\pi(5-2)^2(18)$
$\pi(18)^2(5)-\pi(18)^2(2)$
$\pi(5)^2(18)-\pi(2)^2(18)$
$\pi(18)^2(5-2)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Cylinder Geometry" ], "new_concepts": [ "Hollow Cylinder Volume" ], "current_concepts": [ "Cylinder Geometry", "Hollow Cylinder Volume" ] } ## Identify the geometric components and dimensions $$ \begin{aligned} &\text{Outer cylinder radius } (R) = 5 \ &\text{Inner cylinder radius } (r) = 2 \ &\text{Height of both cylinders } (h) = 18 \end{aligned} $$ ## Formulate the volume of the shaded region $$ \begin{aligned} V_{\text{shaded}} &= V_{\text{outer}} - V_{\text{inner}} \ V_{\text{shaded}} &= \pi R^2 h - \pi r^2 h \ V_{\text{shaded}} &= \pi (5)^2 (18) - \pi (2)^2 (18) \end{aligned} $$ ## Match with the given options $$ \pi(5)^2(18) - \pi(2)^2(18) $$

$\pi(5-2)^2(18)$

$\pi(18)^2(5) - \pi(18)^2(2)$

$\pi(5)^2(18) - \pi(2)^2(18)$

$\pi(18)^2(5-2)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Hollow Cylinder Volume" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the geometric components and dimensions

Formulate the volume of the shaded region

Match with the given options

Answer: