what is the height of the cone below?

$v = 45\text{ in.}^3$
$b = 5\text{ in.}^2$

* 3 in.
* 9 in.
* 27 in.
* 75 in.

Question

what is the height of the cone below?

$v = 45\text{ in.}^3$
$b = 5\text{ in.}^2$

* 3 in.
* 9 in.
* 27 in.
* 75 in.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Volume of a Cone" ], "new_concepts": [], "current_concepts": [ "Volume of a Cone" ] } ## State the volume formula for a cone $$ V = \frac{1}{3} \cdot B \cdot h $$ ## Substitute the given values into the formula $$ 45 = \frac{1}{3} \cdot 5 \cdot h $$ ## Solve for the height $$ \begin{aligned} 45 &= \frac{5}{3}h \ h &= 45 \cdot \frac{3}{5} \ h &= 27\text{ in.} \end{aligned} $$

(A) 3 in.

(B) 9 in.

(C) 27 in.

(D) 75 in.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Cone" ] }

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QUESTION IMAGE

Question

Explanation:

State the volume formula for a cone

Substitute the given values into the formula

Solve for the height

Answer: