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9-12 Integrated Math 3 Unit 1 Lesson 14

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Unit 1, Lesson 14

Prisms and Pyramids

$Course Icon$

Integrated Math 3

Practice

Problem 1

Give each solid a geometric name. Be as precise as you can.

<p>7 sided solid. Hexagon with 6 rectangles meeting on the left side of the solid.<br>
</p> — A

<p>5 sided solid. Two triangles and 3 rectangles.<br>
</p> — B

<p>An oblique cone, no units labeled. A dotted line representing the height of the cone is drawn perpendicular to the plane in which the base lies.</p> — C

Problem 2

Each set of two-dimensional shapes is the complete list of faces from a particular solid. Match each set of shapes with the solid they came from.

2 congruent triangles and 3 rectangles

4 triangles and 1 rectangle

2 squares and 4 congruent parallelograms

4 congruent, equilateral triangles

right triangular prism
oblique square prism
triangular pyramid
rectangular pyramid

Problem 3

These 3 congruent square pyramids can be assembled into a cube with side length 1 foot. What is the volume of each pyramid?

<p>Rectangular pyramid </p>

<p>Rectangular pyramid </p>

<p>Rectangular pyramid </p>

Problem 4

ForLesson 13: Prisms Practice

A prism has a height of 4 inches and a volume of 120 cubic inches. Select all figures that could be the base for this prism.

a 5 inch by 6 inch rectangle
a square with side length 5 inches
a circle with radius 5 inches
a star-shaped base with area 30 square inches
a right triangle with legs 5 inches and 12 inches

Problem 5

ForLesson 13: Prisms Practice

This prism has a right triangle for a base. The volume of the prism is 54 cubic units. What is the value of \(h\)?

<p>Prism with base that is triangle A, B C. Angle A, C B is a right angle. C A, length 4. A, B length 5. Second base triangle D E F, Angle D F E is a right angle. C F, length h.</p>

Problem 6

ForLesson 12: Cross-Sections and Volume

This solid has curved sides. All cross-sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 5 units. What is the volume of this solid?

<p>Solid with curved sides. Top and bottom bases are squares, side lengths = 3.</p>

Problem 7

ForLesson 11: Cylinder Volumes

Find the volume of each solid.

a cylinder with radius 3 inches and height 2 inches
a hexagonal prism whose base has area 4.5 square centimeters and whose height is 7 centimeters
a prism 5 feet tall whose base is a right triangle with leg lengths \(\frac32\) feet and 9 feet

Problem 8

ForLesson 5: Scaling and Area

A circle with an area of \(\pi\) square units is dilated using a scale factor of 5. What is the area of the dilated circle?