Geometry Unit 6: Area and Volume

Areas of polygons, volumes and surface areas of cylinders, pyramids, cones and spheres, density and composite solids. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Volume of cylindersNo calculator

A can is a cylinder 10 centimeters tall with a radius of 3 centimeters. How much does it hold, in cubic centimeters?

1. $60\pi$
2. $180\pi$
3. $90\pi$
4. $30\pi$

Question 2

Volume of conesNo calculator

A paper cup is a cone 8 centimeters deep, and its circular rim has radius 6 centimeters. How much does it hold, in cubic centimeters?

1. $96\pi$
2. $48\pi$
3. $288\pi$
4. $32\pi$

Question 3

Volume of spheresCalculator

A spherical tank has a diameter of 12 feet. What is its volume, to the nearest cubic foot?

1. $905$
2. $904$
3. $7{,}238$
4. $452$

Question 4

Surface areaNo calculator

What is the surface area of a sphere with radius 5?

1. $20\pi$
2. $25\pi$
3. $100\pi$
4. $\frac{500\pi}{3}$

Question 5

Volume of pyramidsNo calculator

A pyramid has a square base with side 10 and a height of 12. What is its volume?

1. $1200$
2. $400$
3. $600$
4. $240$

Question 6

DensityNo calculator

A block of wood measures 4 cm by 5 cm by 10 cm and has a mass of 140 grams. What is its density, in grams per cubic centimeter?

1. $0.7$
2. $2800$
3. $1.43$
4. $7$

Question 7

Area of polygonsNo calculator

A trapezoid has bases 7 and 13 and height 6. What is its area?

1. $120$
2. $26$
3. $546$
4. $60$

Question 8

Area of polygonsNo calculator

A floor tile is a regular hexagon whose sides are 4 inches long. What is its area, in square inches?

1. $48\sqrt{3}$
2. $24\sqrt{3}$
3. $96$
4. $6\sqrt{3}$

Question 9

Cones and cylindersNo calculator

A cone and a cylinder have the same base and the same height. The cylinder holds 54 cubic inches. How much does the cone hold?

1. $162$
2. $18$
3. $27$
4. $54$

Question 10

Composite solidsNo calculator

A solid is a cylinder of radius 2 and height 5 with a hemisphere of radius 2 on top. What is its volume?

1. $\frac{76\pi}{3}$
2. $28\pi$
3. $\frac{92\pi}{3}$
4. $20\pi$

Question 11

Scaling solidsNo calculator

Every dimension of a box is doubled. By what factor is its volume multiplied?

1. $4$
2. $2$
3. $8$
4. $6$

Question 12

Solids of rotationNo calculator

A 3-by-7 rectangle is rotated about its 7-unit side. What is the volume of the solid it sweeps out?

1. $21\pi$
2. $147\pi$
3. $63\pi$
4. $42\pi$