Pyramids and Cones Practice

Classify the solid by its bases and lateral faces.

Use h for volume and include the factor 1/3.

Surface area uses slant height, not perpendicular height.

Label h and ℓ before selecting a formula.

Use the same-base, same-height one-third relationship.

Multiply base area by perpendicular height, then divide by 3.

Multiply base area by perpendicular height, then divide by 3.

Multiply base area by perpendicular height, then divide by 3.

Multiply base area by perpendicular height, then divide by 3.

Multiply base area by perpendicular height, then divide by 3.

Find lateral area, then add one square base.

Use half the base perimeter times slant height.

Find lateral area, then add one square base.

Use half the base perimeter times slant height.

Find lateral area, then add one square base.

Square the radius, multiply by h, and divide by 3.

Square the radius, multiply by h, and divide by 3.

Square the radius, multiply by h, and divide by 3.

Square the radius, multiply by h, and divide by 3.

Square the radius, multiply by h, and divide by 3.

Use slant height for the curved area, then add one base.

The lateral-area formula is πrℓ.

Use slant height for the curved area, then add one base.

The lateral-area formula is πrℓ.

Use slant height for the curved area, then add one base.

Use the radius and perpendicular height as legs; slant height is the hypotenuse.

Use the radius and perpendicular height as legs; slant height is the hypotenuse.

Use the radius and perpendicular height as legs; slant height is the hypotenuse.

Use the radius and perpendicular height as legs; slant height is the hypotenuse.

Use the radius and perpendicular height as legs; slant height is the hypotenuse.

Convert circumference to radius before using volume.

Cancel π, then isolate h.

Find total volume, then divide by the constant volumetric rate.

Multiply volume by 3, then divide by base area.

Use lateral area πrℓ and cancel π.

Use one common linear scale factor for height and radius.

Cube a linear scale factor when comparing volumes.

Find both cone volumes with their own dimensions, then subtract.

Find both cone volumes with their own dimensions, then subtract.

Find both cone volumes with their own dimensions, then subtract.

Subtract both cone volumes from the enclosing cylinder.

Subtract both cone volumes from the enclosing cylinder.

Add nonoverlapping component volumes; the shared circle has no volume.

The pyramid occupies one third, so two thirds of the matching prism remains.

For equal radii, combine the heights before applying the cone formula.

Square the radius scale and multiply by the height scale.

Use the one-third relationship before calculating dimensions.

Separate volume formulas from surface-area formulas.

Decide which surfaces are physically present before adding a base.

Square a uniform linear factor for area and cube it for volume.