Back to Exercise: Use volume formulas to solve

Exercises: Use Volume Formulas to Solve Problems

Grade 10·22 problems·~40 min·Common Core Math - HS Geometry·standard·hsg-gmd-a-3

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Recall / Warm-Up

Which formula gives the volume of a cone with base radius $r$ and height $h$ ?

$V = \pi r^2 h$

$V = \frac{1}{3}\pi r^2 h$

$V = \frac{4}{3}\pi r^3$

$V = \frac{1}{3}Bh$

A square pyramid has a square base with side length $s$ and height $h$ . Which expression correctly represents the base area $B$ to use in the volume formula $V = \frac{1}{3}Bh$ ?

$B = s$

$B = 4s$

$B = s^2$

$B = \frac{1}{2}s^2$

A container holds 2 m³ of liquid. How many liters is this? (Use: 1 m³ = 1,000 L)

2 liters

200 liters

2,000 liters

2,000,000 liters

Fluency Practice

A cylinder has radius 4 cm and height 11 cm. Find its volume. Express your answer in terms of $\pi$ (e.g., write "176π cm³").

A cylindrical water tank has a diameter of 6 m and a height of 5 m. Find its volume in cubic meters, then convert to liters. Round to the nearest liter. (Use: 1 m³ = 1,000 L)

A square pyramid has a base side length of 9 cm and a height of 8 cm. What is its volume in cm³?

A sphere has a radius of 6 cm. Find its volume. Express your answer in terms of $\pi$ .

$A grain silo made of a cylinder (height 12 m, radius 5 m) topped by a cone (height 3 m, same radius). Dimension labels mark each component.$

A grain silo consists of a cylinder topped with a cone. The cylinder has radius 5 m and height 12 m. The cone has the same radius and a height of 3 m. Find the total volume of the silo in terms of $\pi$ .

A cone with radius 6 cm and height 10 cm is carved out of the top of a cylinder with the same radius and height. What volume of material remains? Express your answer in terms of $\pi$ .

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