Formulas: 3D Shapes [TEKS Tools Grade 8]

This post specifically looks at how formulas can be used solve problems involving volume and surface area. Read more about TEKS Tools and their rationale here.

Formulas

Formulas account for around 38% of each 8th grade STAAR test. These formulas are applied to solve problems related to volume, surface area, triangles, similar shapes, linear relationships, and finances.

The main function of a formula is to understand the relationship between quantities. In fourth grade, students were first introduced to the formulas for area and perimeter of squares and rectangles. In fifth grade, they were introduced to the formula for volume of a rectangular prism. In sixth grade, the formulas for area of a triangle, parallelogram, and trapezoid are explored. In 7th grade, students are introduced to surface area and to circle geometry, exploring π (pi), circumference, and area. Now in 8th grade, students stabilize their previous learning about linear relationships, surface area, volume (including composite shapes), and finances while beginning to explore geometric concepts such as the Pythagorean Theorem.

Area

Formulas are used to calculate area, including irrational side lengths

8.2B - approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

2023-9: an area was given, students had to estimate the side length

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Volume

8.6A - describe the volume formula V = Bh of a cylinder in terms of its base area and its height

2023-31: the volume and radius were given, students had to identify an equation to find the height

2024-12: the radius and height were given, students had to identify an equation to find the volume

2025-25: the diameter and height were given, students had to write an equation to find the volume

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8.7A - solve problems involving the volume of cylinders, cones, and spheres

2023-14: a composite shape was given, students had to find the volume

2023-27: the radius and height were given, students had to estimate the volume of a cone

2024-1: the diameter was given, students had to estimate the volume of a sphere

2024-30: the radius and height were given, students had to calculate the volume of a cone in terms of pi

2025-21: the diameter was given, students had to find the volume of a sphere in terms of pi

2025-35: the radius and height were given, students had to estimate the volume of a cone

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Surface Area

Lateral and total surface area, first introduced in 7th grade without formulas, are built upon in 8th grade through the use of specific formulas.

8.7B - use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

2023-6: a rectangular prism was given, students had to find the other rectangular prism with the same total surface area

2023-25: the height and area of the base were given, students had to calculate the total surface area

2024-8: a triangular prism was given, students had to calculate the total surface area

2024-25: a rectangular prism was given, students had to calculate the total surface area

2025-9: the lateral surface area and base side lengths for a triangular prism were given, students had to calculate the height

2025-37: a rectangular prism was given, students had to calculate the total surface area