Willhite - Exploring Solids Review

Circumference, Arc Length, Area of Circles, and Area of Sectors

100

The circumference of a circle is 48in. Find the radius.

24/pi or 7.64

200

The diameter of a circle is 36yds. Find the area of the circle. Round to the nearest hundredth.

1017.88yds²

300

Find the arc length of arc AB with a radius of 10m and a central angle of 72 degrees. Round to the nearest hundredth.

12.57m

400

Find the area of the sector with a central angle of 80 degrees and a radius of 6cm. Round to the nearest hundredth.

25.13cm2

500

The measure of arc TS is 40 degrees. The circle has a diameter of 18in. Find the area of the circle. 

254.47in²

Area of Regular Polygons

100

Write the equation for finding the area of a hexagon.

Area - 1/2 * apothem * perimeter of polygon

200

What is the area of a square with a side length of 8m and an apothem length of 4m.

64m²

300

Find the perimeter of a regular triangle with an area of 48cm² and an apothem measuring 8cm.

12cm (or 4cm per side)

400

Find the area of a pentagon with a length of 18in (from the center to a vertex) and a base of 24in. 

900in²

500

Find the area of the octagon with a length from the center to a vertex of 39mm. 

4302mm²

Explore Solids, Volume of Spheres, & Surface Area of Spheres

100

Is this a polyhedron? (Cheese)

No.

200

How many edges are on this polygon if there are 6 faces and 8 vertices?

12 edges

300

What is the volume of a sphere with a radius of 27cm?

82447.96cm³

400

What is the surface area of a sphere with a diameter of 2.41in?

18.25in²

500

What is the volume of a sphere with a circumference of 300m?

455945.33m³

Volume of Prisms & Cylinders

100

How many bases does a prism have?

2

200

Find the volume of the rectangular prism with a length of 4, a height of 2, and a width of 6.

48

300

Find the volume of a cylinder with a radius of 9cm and a height of 10cm.

2544.69cm³

400

Find the volume of a triangular prism when the height of the triangular base is 8m, the base of the triangle is 7m, and the height of the solid is 6m. 

168m³

500

Find the volume of the regular hexagonal prism with an apothem of 11cm and a side length of 5cm. The height of the solid is 14cm. 

2310cm³

Volume of Pyramids & Cones

100

How many bases do pyramids and cones have?

1

200

What is the volume of a cone with a radius of 21cm and a height of 12cm?

5541.77cm³

300

What is the volume of a square pyramid with a side length of 13in and the height of the solid measuring 10in?

563.33in³

400

What is the volume of a regular heptagonal (7 sides) pyramid with an apothem of 6mm, a side length of 12.5mm, and the height of the solid measuring 8mm?

700mm³

500

What is the radius of a cone when the volume is 40pi if you know the height is 5cm?

4.9cm