Volume of Prisms and Pyramids

Front

What is the formula for the volume of a prism?

Back

Volume = Base Area × Height

Tags

CCSS.7.G.B.6

Front

What is the formula for the volume of a pyramid?

Back

Volume = (1/3) × Base Area × Height

Tags

CCSS.HSG.GMD.A.3

Front

Define a prism.

Back

A solid shape with two parallel, congruent bases connected by rectangular faces.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Front

Define a pyramid.

Back

A solid shape with a polygonal base and triangular faces that meet at a single point (the apex).

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Front

What is the base area of a triangular prism with a base of 5 cm and height of 4 cm?

Back

Base Area = (1/2) × base × height = (1/2) × 5 × 4 = 10 cm²

Tags

CCSS.7.G.B.6

Front

Calculate the volume of a rectangular prism with a length of 3 cm, width of 4 cm, and height of 5 cm.

Back

Volume = Length × Width × Height = 3 × 4 × 5 = 60 cm³

Tags

CCSS.7.G.B.6

Front

What is the height of a pyramid if the volume is 30 cm³ and the base area is 10 cm²?

Back

Height = (Volume × 3) / Base Area = (30 × 3) / 10 = 9 cm

Tags

CCSS.HSG.GMD.A.3

Front

What is the volume of a square pyramid with a base side of 6 cm and height of 9 cm?

Back

Volume = (1/3) × Base Area × Height = (1/3) × (6 × 6) × 9 = 108 cm³

Tags

CCSS.HSG.GMD.A.3

Front

If a triangular pyramid has a base area of 12 cm² and a height of 5 cm, what is its volume?

Back

Volume = (1/3) × Base Area × Height = (1/3) × 12 × 5 = 20 cm³

Tags

CCSS.HSG.GMD.A.3

Front

What is the volume of a cylinder with a radius of 3 cm and height of 7 cm?

Back

Volume = π × radius² × height = π × 3² × 7 ≈ 65.97 cm³

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3