Non-Cubic Prisms

Help Questions

Math › Non-Cubic Prisms

Questions 1 - 10

Find the volume of the following triangular prism:

Triangular_prism

$108\sqrt{3}m^3$

$98\sqrt{3}m^3$

$88\sqrt{3}m^3$

$118\sqrt{3}m^3$

$128\sqrt{3}m^3$

Explanation

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

Find the volume of the following triangular prism:

Triangular_prism

$108\sqrt{3}m^3$

$98\sqrt{3}m^3$

$88\sqrt{3}m^3$

$118\sqrt{3}m^3$

$128\sqrt{3}m^3$

Explanation

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

Find the surface area of the following triangular prism.

Half_box

$144 + 54\sqrt{2} m^2$

$144 + 54\sqrt{3} m^2$

$54 + 144\sqrt{2} m^2$

$54 + 144\sqrt{3} m^2$

$144 + 52\sqrt{2} m^2$

Explanation

The formula for the surface area of a triangular prism is:

$SA = 2 (base) + lateral\ area$

$SA = 2 \cdot \left(\frac{1}{2}\right)(l)(w) + (l+w+y)(h)$

Where is the length of the triangle, is the width of the triangle, is the hypotenuse of the triangle, and is the height of the prism

Use the formula for a triangle to solve for the length of the hypotenuse:

$s-s-s\sqrt{2}$

$6-6-6\sqrt{2}$

Plugging in our values, we get:

$SA = (6m)(6m) + (6m+6m+6\sqrt{2}m)(9m)$

$SA = (6m)(6m) + (12m + 6\sqrt{2}m)(9m)$

$SA = 36m^2 + 108m^2 + 54\sqrt{2}m^2 = 144 + 54\sqrt{2} m^2$

Find the surface area of the following triangular prism.

Half_box

$144 + 54\sqrt{2} m^2$

$144 + 54\sqrt{3} m^2$

$54 + 144\sqrt{2} m^2$

$54 + 144\sqrt{3} m^2$

$144 + 52\sqrt{2} m^2$

Explanation

The formula for the surface area of a triangular prism is:

$SA = 2 (base) + lateral\ area$

$SA = 2 \cdot \left(\frac{1}{2}\right)(l)(w) + (l+w+y)(h)$

Where is the length of the triangle, is the width of the triangle, is the hypotenuse of the triangle, and is the height of the prism

Use the formula for a triangle to solve for the length of the hypotenuse:

$s-s-s\sqrt{2}$

$6-6-6\sqrt{2}$

Plugging in our values, we get:

$SA = (6m)(6m) + (6m+6m+6\sqrt{2}m)(9m)$

$SA = (6m)(6m) + (12m + 6\sqrt{2}m)(9m)$

$SA = 36m^2 + 108m^2 + 54\sqrt{2}m^2 = 144 + 54\sqrt{2} m^2$

Find the surface area of the following triangular prism.

Triangular_prism

$216 + 18\sqrt{3}m^2$

$216 + 216\sqrt{3}m^2$

$18 + 18\sqrt{3}m^2$

$218 + 16\sqrt{3}m^2$

$216 + 16\sqrt{3}m^2$

Explanation

The formula for the surface area of an equilateral, triangular prism is:

$SA = 2\left(\frac{s^2\sqrt{3}}{4}\right)+(3s)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$SA = 2\left(\frac{(6m)^2\sqrt{3}}{4}\right)+(3)(6m)(12m)$

$SA = 216 + 18\sqrt{3}m^2$

Find the surface area of the following triangular prism.

Triangular_prism

$216 + 18\sqrt{3}m^2$

$216 + 216\sqrt{3}m^2$

$18 + 18\sqrt{3}m^2$

$218 + 16\sqrt{3}m^2$

$216 + 16\sqrt{3}m^2$

Explanation

The formula for the surface area of an equilateral, triangular prism is:

$SA = 2\left(\frac{s^2\sqrt{3}}{4}\right)+(3s)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$SA = 2\left(\frac{(6m)^2\sqrt{3}}{4}\right)+(3)(6m)(12m)$

$SA = 216 + 18\sqrt{3}m^2$

Find the volume of the following triangular prism.

Half_box

Explanation

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

Find the volume of the following triangular prism.

Half_box

Explanation

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

David wants to paint the walls in his bedroom. The floor is covered by a $10\ ft \times 16\ ft$ carpet. The ceiling is $8\ ft$ tall. He selects a paint that will cover $75\ ft^2$ per quart and $300\ ft^2$ per gallon. How much paint should he buy?

1 gallon and 2 quarts

3 quarts

2 gallons and 1 quart

1 gallon

1 gallon and 1 quart

Explanation

Find the surface area of the walls: SAwalls = 2lh + 2wh, where the height is 8 ft, the width is 10 ft, and the length is 16 ft.

This gives a total surface area of 416 ft2. One gallon covers 300 ft2, and each quart covers 75 ft2, so we need 1 gallon and 2 quarts of paint to cover the walls.

1 gallon and 2 quarts

3 quarts

2 gallons and 1 quart

1 gallon

1 gallon and 1 quart

Explanation

Find the surface area of the walls: SAwalls = 2lh + 2wh, where the height is 8 ft, the width is 10 ft, and the length is 16 ft.

This gives a total surface area of 416 ft2. One gallon covers 300 ft2, and each quart covers 75 ft2, so we need 1 gallon and 2 quarts of paint to cover the walls.

Page 1 of 3

Return to subject