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Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

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Can I use my own voice with Goblins?

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What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

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Does Goblins support English Language Learners?

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G-GMD.A.2

(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Example Problems

The base of a solid is the region enclosed by the graphs of

y = \ln(x)

and

y = 0.1x^3 - 0.5x^2

, between

x = 2

and

x = 5

.

Cross sections of the solid perpendicular to the x-axis are rectangles whose height is

6 - x

.

What definite integral gives the volume of the solid?

The base of a solid is the region enclosed by the graphs of

y = \ln(x + 2)

and

y = \frac{x}{4}

, between the y-axis and

x = 4

.

Cross sections of the solid perpendicular to the x-axis are rectangles whose height is

5 - x

.

What definite integral gives the volume of the solid?

The base of a solid is the region enclosed by the graphs of

y = \sin(x)

and

y = 4 - \sqrt{x}

, between

x = 2

and

x = 7

.

Cross sections of the solid perpendicular to the x-axis are rectangles whose height is

2x

.

What definite integral gives the volume of the solid?

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