Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.73 Work to Pump Fluids Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.73 Work to Pump Fluids. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.73 Work to Pump Fluids - Choose the correct slice, distance, and density expression for pumping liquid from a tank. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.73 Work to Pump Fluids skill assessments:

Problem 1Difficulty: Mastery

A tank has horizontal slice area A(y) = π(4 - y/2)² m² for 0 ≤ y ≤ 6. Liquid occupies 2 ≤ y ≤ 6 and has mass density ρ(y) = 980 + 40(6 - y) kg/m³. It is pumped to y = 7.5 m. Use g = 9.8 m/s². Which integral gives the work?

AW = ∫_2⁶ (980 + 40(6 - y))π(4 - y/2)²(7.5 - y) dy

BW = ∫_0⁶ (980 + 40(6 - y))(9.8)π(4 - y/2)²(7.5 - y) dy

CW = ∫_2⁶ (980 + 40y)(9.8)π(4 - y/2)²(7.5 - y) dy

DW = ∫_2⁶ (980 + 40(6 - y))(9.8)π(4 - y/2)²(7.5 - y) dy

Solution & Explanation:The area function is already given, so use it directly. Because ρ(y) is mass density, multiply by g; the fluid layer is 2 to 6 and the lifting distance to the outlet is 7.5 - y.

Problem 2Difficulty: Mastery

A tank has annular horizontal slices. At height y, the outer radius is R(y) = √(25 - (y - 5)²) ft and the inner radius is 1 ft. A liquid of weight density 64 lb/ft³ occupies 2 ≤ y ≤ 8 and is pumped to y = 11. Which integral gives the work?

AW = ∫_2⁸ 64π(25 - (y - 5)²)(11 - y) dy

BW = ∫_2⁸ 64π(√(25 - (y - 5)²) - 1)²(11 - y) dy

CW = ∫_2⁸ 64π((25 - (y - 5)²) - 1²)(11 - y) dy

DW = ∫_2⁸ 64π((25 - (y - 5)²) - 1²)(8 - y) dy

Solution & Explanation:For an annular slice, area is π(R² - r²). Since R(y)² = 25 - (y - 5)² and the inner radius is 1, the area factor is π((25 - (y - 5)²) - 1²). The outlet height gives 11 - y.

Problem 3Difficulty: Mastery

A tank in SI units has liquid mass density ρ(y), horizontal slice area A(y), liquid bounds a ≤ y ≤ b, and outlet height c with c > b. Which expression has units of joules for the pumping work?

AW = ∫_a^b ρ(y)A(y)(c - y) dy

BW = ∫_a^b ρ(y)gA(y)(c - y) dy

CW = ∫_a^b ρ(y)gA(y)(b - y) dy

DW = ∫_a^c ρ(y)gA(y)(c - y) dy

Solution & Explanation:In SI units, mass density must be multiplied by g to produce weight density. The bounds are the liquid bounds a to b, and the distance to the outlet is c - y.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Choose the correct slice, distance, and density expression for pumping liquid from a tank. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.).