Topics
10. Modeling in 2 & 3 Dimensions
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United States of AmericaVA
Geometry

10.04 Cones and pyramids

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

We wish to find the surface area of the right pyramid pictured.

A right pyramid have a square base and triangular faces extend from each side of the square to the apex. The length of the base is labeled $10$10 mm each. The perpendicular height is marked with a line from the apex to the center of the base, and is labeled $8$8 mm. A small blue square at the intersection of the perpendicular height and square base indicates a right angle. The non-visible part of the right pyramid is represented as dashed lines.
a

Find the slant height of the pyramid.

Round your answer to two decimal places.

b

Using the rounded slant height found in part (a), find the surface area of the right pyramid. Include all faces in your calculations.

Round your answer to two decimal places.

Medium
3 min

Find the surface area of the cone pictured.

Medium
2 min

A square pyramid has a surface area of $310$310 cm2. The area of its square base is $49$49 cm2.

Medium
3 min

Find the surface area of the following right pyramid. Include all faces in your calculations.

Medium
1 min
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Outcomes

G.DF.1

The student will create models and solve problems, including those in context, involving surface area and volume of rectangular and triangular prisms, cylinders, cones, pyramids, and spheres.

G.DF.1b

Create models and solve problems, including those in context, involving surface area of threedimensional figures, as well as composite three-dimensional figures.

G.DF.1c

Solve multistep problems, including those in context, involving volume of three-dimensional figures, as well as composite three-dimensional figures.

G.DF.1d

Determine unknown measurements of three-dimensional figures using information such as length of a side, area of a face, or volume.

G.DF.2

The student will determine the effect of changing one or more dimensions of a three-dimensional geometric figure and describe the relationship between the original and changed figure.

G.DF.2a

Describe how changes in one or more dimensions of a figure affect other derived measures (perimeter, area, total surface area, and volume) of the figure.

G.DF.2b

Describe how changes in surface area and/or volume of a figure affect the measures of one or more dimensions of the figure.

G.DF.2c

Solve problems, including those in context, involving changing the dimensions or derived measures of a three-dimensional figure.

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