Geometry Answers

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Find the number of vertices of a polyhedron made up of 8 triangles and 6 octagons.

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1. Find the number of vertices of a polyhedron made up of 8 triangles and 6 octagons.

2. Find the surface area of a right prism if height = 3 in, base = 4 in, and length = 3.5 in.

3. A right prism has bases which are regular octagons of side length 4 cm. Its height is 5 cm. Find its surface area.

4. Find the height of a cylindrical water tank that has a surface area of 120 (pi) and a diameter of 10 m.

5. Calculate the volume of a regular hexagonal pyramid that has a slant height of 35 cm and a base side length of 4 cm.

6. Find the surface area of a square-based pyramid with a slant height of 7 ft and a base side of 5 ft.

7. Find the surface area of a right cone if base = 15 cm and slant height = 9 cm.

8. A cylindrical can is 20 cm in diameter and 16 cm in height. You want to reduce the diameter of the can to 16 cm. What must the height be if the new can still has the same volume?

1. In a square pyramid, the perimeter of the base is 72 m. The surface area is 864 m squared. Find the slant height of the pyramid.

2. A right pentagonal prism has a height of 6 in. The regular pentagon has a side length of 2 in. Find the surface area of the prism.

3. A machinist drilled a conical hole into a cube of metal. If the cube has sides of length 5 cm, what is the volume of the metal after the hole is drilled?

4. Two similar cylinders have a surface area of 96(pi) square ft and 150(pi) square feet. The height of each cylinder is equal to its diameter. Find the dimensions (radius and height) of one cylinder and use their scale factor to find the dimensions of the other cylinder.

In a isosceles trapezoid the legs are equal to two and the upper base is equal to 2 as well. what is the length of the downward base?

Find the area bounded by y = 5 + 4x − x2, the x-axis and the ordinates x = 1 and x = 4.

a. 24 unit^2
b. 19 unit^2
c. 2 unit^2
d. 32 unit^2

Determine the area under the curve y = ex between x = (-)2 and x = 3.

a. 19.95 unit^2
b. 19.90 unit^2
c. 19.75 unit^2
d. 11.95 unit^2

Calculate the area bounded by the curve y = (−)6x2 + 24x10, the x-axis and the ordinates x = 0 and x = 4.

a. 10 unit^2
b. 104 unit^2
c. 77 unit^2
d. 134 unit^2

Determine the area bounded by the curve y=3x2 + 6x + 8, the x-axis and the ordinates x=1 and x =3.

a. 6 unit^2
b. 6 unit^2
c. 66 unit^2
d. 65 unit^2

find the surface area of a right octagonal pyramid with height 2.5 yards, and its base has apothem length 1.5 yards