q. a bowl is in the shape of a half sphere. how many cubic inches can the bowl hold if its diameter measures 18 inches? use 3.14 for $\pi$ and round your answer to the nearest whole number. the formula for volume of a sphere is $v = \frac{4}{3}\pi r^3$

a. 4,578
b. 3,052
c. 1,526
d. 763

Question

q. a bowl is in the shape of a half sphere. how many cubic inches can the bowl hold if its diameter measures 18 inches? use 3.14 for \$\pi\$ and round your answer to the nearest whole number. the formula for volume of a sphere is \$v = \frac{4}{3}\pi r^3\$

a. 4,578
b. 3,052
c. 1,526
d. 763

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Word Problems", "Rounding Numbers" ], "new_concepts": [ "Volume of Hemisphere", "Sphere Volume Formula" ], "current_concepts": [ "Word Problems", "Rounding Numbers", "Volume of Hemisphere", "Sphere Volume Formula" ] } ## Find the radius of the bowl Using the **Word Problems** knowledge point $$ \begin{aligned} d &= 18\text{ inches}\ r &= \frac{d}{2} = \frac{18}{2} = 9\text{ inches} \end{aligned} $$ ## Calculate the volume of a full sphere Using the **Word Problems** knowledge point $$ \begin{aligned} V_{\text{sphere}} &= \frac{4}{3}\pi r^3\ V_{\text{sphere}} &= \frac{4}{3} \times 3.14 \times 9^3\ V_{\text{sphere}} &= \frac{4}{3} \times 3.14 \times 729\ V_{\text{sphere}} &= 4 \times 3.14 \times 243 = 3052.08\text{ cubic inches} \end{aligned} $$ ## Calculate the volume of the half sphere Using the **Word Problems** knowledge point $$ \begin{aligned} V_{\text{bowl}} &= \frac{1}{2} V_{\text{sphere}}\ V_{\text{bowl}} &= \frac{1}{2} \times 3052.08 = 1526.04\text{ cubic inches} \end{aligned} $$ ## Round to the nearest whole number Using the **Rounding Numbers** knowledge point $$ \begin{aligned} 1526.04 &\approx 1526 \end{aligned} $$

(A) 4,578

(B) 3,052

(C) 1,526

(D) 763

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

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QUESTION IMAGE

Question

Explanation:

Find the radius of the bowl

Calculate the volume of a full sphere

Calculate the volume of the half sphere

Round to the nearest whole number

Answer: