Decimals and Volume, Surface Area of Rectangular Prism & Pyramid

Calculate the surface area of a square pyramid with a base side length of 6 cm and a slant height of 10 cm.

• 96 cm²

• 120 cm²

• 156 cm²

• 180 cm²

Answer explanation

The surface area of a square pyramid is given by SA = base area + lateral area. Base area = 6 cm * 6 cm = 36 cm². Lateral area = 2 * base side * slant height = 2 * 6 cm * 10 cm = 120 cm². Total SA = 36 cm² + 120 cm² = 156 cm².

A net of a square pyramid is shown. If the base side length is 4 cm and the slant height is 6 cm, what is the surface area?

• 64 cm²

• 72 cm²

• 80 cm²

• 88 cm²

Answer explanation

The surface area of a square pyramid is given by SA = base area + lateral area. Base area = 4 cm * 4 cm = 16 cm². Lateral area = 2 * base side * slant height = 2 * 4 cm * 6 cm = 48 cm². Total SA = 16 cm² + 48 cm² = 64 cm².

What is the area of the composite shape?

• 40ft²

• 9ft²

• 49ft²

• 61ft²

Answer explanation

To find the area of the composite shape, calculate the areas of the individual components and sum them. The total area is 61ft², making it the correct choice.

Tags

CCSS.6.G.A.1

What is the volume of the composite figure?

• 525 cubic cm

• 47 cubic cm

• 2,990,400 cubic cm

• 829 cubic cm

Answer explanation

To find the volume of the composite figure, calculate the volumes of its individual parts and sum them. The correct total volume is 525 cubic cm, matching the first answer choice.

Tags

CCSS.5.MD.C.3

CCSS.5.MD.C.5

CCSS.5.MD.C.4

CCSS.5.MD.C.6

A square pyramid is covered with decorative wrapping paper with no overlap.  The net of the box is shown on the right.  How many square centimeters of wrapping paper are needed to cover the surfaces of the box? 

• 108 cm²

• 324 cm²

• 180 cm²

• 432 cm²

Answer explanation

To find the surface area of the square pyramid, calculate the area of the base (a^2) and the area of the four triangular faces (2*a*l, where l is the slant height). The total area is 180 cm², which is the required wrapping paper.

Tags

CCSS.6.G.A.4

CCSS.6.G.A.1

I have 1 face that is a rectangle and 4 faces that are triangles

• Triangular Prism

• Rectangular Pyramid

• Triangular Pyramid

• Rectangular Prism

Answer explanation

The shape described has 1 rectangular face and 4 triangular faces, which matches the definition of a Rectangular Pyramid. The base is a rectangle, and the sides are triangles, confirming this choice.

Tags

CCSS.5.MD.C.3

CCSS.5.MD.C.5

How many faces, vertices, and edges do I have?

• 2 Faces

  5 Edges

  4 Vertices

• 3 Faces

  5 Edges

  4 Vertices

• 5 Faces

  8 Edges

  5 Vertices

• 3 Faces

  6 Edges

  3 Vertices

Answer explanation

The correct choice is 5 Faces, 8 Edges, and 5 Vertices, which corresponds to a polyhedron like a cube. This satisfies Euler's formula: V - E + F = 2 (5 - 8 + 5 = 2).

Tags

CCSS.6.G.A.4

How many faces are on a cube?

• 3

• 4

• 5

• 6

Answer explanation

A cube has 6 faces, each of which is a square. This is a defining characteristic of a cube, making the correct answer 6.

Tags

CCSS.6.G.A.4

13.16 + 5.90

• 18.86

• 18.06

• 19.06

• 19.00

Answer explanation

To solve 13.16 + 5.90, align the decimal points and add: 13.16 + 5.90 = 19.06. Thus, the correct answer is 19.06.

Tags

CCSS.6.NS.B.3

27.53 - 8.6

Answer explanation

To solve 27.53 - 8.6, align the decimal points: 27.53 - 8.60 = 18.93. The correct answer is 18.93, not 0.

Tags

CCSS.5.NBT.B.7