drinking cups in the shape of a cone, with dimensions as shown

to the nearest tenth of a cubic inch, what is the volume of each drinking cup?

Question

drinking cups in the shape of a cone, with dimensions as shown

to the nearest tenth of a cubic inch, what is the volume of each drinking cup?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Evaluating Expressions" ], "new_concepts": [ "Volume of a Cone", "Fractional Dimensions" ], "current_concepts": [ "Evaluating Expressions", "Volume of a Cone", "Fractional Dimensions" ] } ## Identify the given dimensions and formula $$ \begin{aligned} &d = 2\frac{3}{4}\text{ in.} = 2.75\text{ in.}\ &r = \frac{d}{2} = 1.375\text{ in.}\ &h = 4\text{ in.}\ &V = \frac{1}{3}\pi r^2 h \end{aligned} $$ ## Calculate the volume of the cone $$ \begin{aligned} &V = \frac{1}{3} \cdot \pi \cdot (1.375)^2 \cdot 4\ &V = \frac{1}{3} \cdot \pi \cdot 1.890625 \cdot 4\ &V = \frac{7.5625}{3}\pi \approx 2.52083\pi \approx 7.9196\text{ cubic inches} \end{aligned} $$ ## Round to the nearest tenth of a cubic inch $$ V \approx 7.9\text{ cubic inches} $$ $7.9\text{ cubic inches}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Cone" ] }

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Question

Explanation:

Identify the given dimensions and formula

Calculate the volume of the cone

Round to the nearest tenth of a cubic inch

Answer: