a cylinder and a cone have the same base and height. the cylinder can hold about $4,712\text{ cm}^3$ of sand. jared says that the cone can hold about $1,178\text{ cm}^3$ of sand. which explains whether jared is correct?

jared is correct because the volume of the cone is less than the volume of the cylinder. the cone holds $4712 - 1178 = 3534\text{ cm}^3$ less sand than the cylinder.

jared is correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{4} = 1178\text{ cm}^3$ of sand.

jared is not correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{3} \approx 1571\text{ cm}^3$ of sand.

jared is not correct because the volume of the cone cannot be found without knowing the radius of the base and the height of the cone.

Question

a cylinder and a cone have the same base and height. the cylinder can hold about $4,712\text{ cm}^3$ of sand. jared says that the cone can hold about $1,178\text{ cm}^3$ of sand. which explains whether jared is correct?

jared is correct because the volume of the cone is less than the volume of the cylinder. the cone holds $4712 - 1178 = 3534\text{ cm}^3$ less sand than the cylinder.

jared is correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{4} = 1178\text{ cm}^3$ of sand.

jared is not correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{3} \approx 1571\text{ cm}^3$ of sand.

jared is not correct because the volume of the cone cannot be found without knowing the radius of the base and the height of the cone.

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", "Volume of a Cone" ], "new_concepts": [ "Volume Relationship between Cylinder and Cone" ], "current_concepts": [ "Cylinder Geometry", "Volume of a Cone", "Volume Relationship between Cylinder and Cone" ] } ## Relate the volume formulas of a cylinder and a cone $$ \begin{aligned} V_{\text{cylinder}} &= \pi r^2 h \ V_{\text{cone}} &= \frac{1}{3} \pi r^2 h = \frac{1}{3} V_{\text{cylinder}} \end{aligned} $$ ## Calculate the expected volume of the cone $$ \begin{aligned} V_{\text{cylinder}} &\approx 4712\text{ cm}^3 \ V_{\text{cone}} &\approx \frac{4712}{3} \approx 1570.67\text{ cm}^3 \approx 1571\text{ cm}^3 \end{aligned} $$ ## Evaluate Jared's claim and select the correct option $$ \begin{aligned} &1178\text{ cm}^3 eq 1571\text{ cm}^3 \implies \text{Jared is not correct.} \ &\text{Correct explanation: Jared is not correct because } V_{\text{cone}} = \frac{4712}{3} \approx 1571\text{ cm}^3. \end{aligned} $$

(A) Jared is correct because the volume of the cone is less than the volume of the cylinder. The cone holds $4712 - 1178 = 3534\text{ cm}^3$ less sand than the cylinder.

(B) Jared is correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{4} = 1178\text{ cm}^3$ of sand.

(C) Jared is not correct because the cone and the cylinder have the same base and height so the cone holds $\frac{4712}{3} \approx 1571\text{ cm}^3$ of sand.

(D) Jared is not correct because the volume of the cone cannot be found without knowing the radius of the base and the height of the cone.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume Relationship between Cylinder and Cone" ] }

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QUESTION IMAGE

Question

Explanation:

Relate the volume formulas of a cylinder and a cone

Calculate the expected volume of the cone

Evaluate Jared's claim and select the correct option

Answer: