A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the height is 5 cm. Find the VOLUME of the tea bag.

Question

anonymous · Answer

Select one:
a. 26.7 cm^3
b. 40 cm^3
c. 36.7 cm^3
d. 24.5 cm^3 Incorrect

mathstudent55 · Answer

|dw:1437759228283:dw|

mathstudent55 · Answer

$\large V_{pyramid} = \dfrac{1}{3}Bh$

The volume of a pyramid is one-third the area of the base times height.

Since your pyramid has a square base, $B = s^2 = (4 ~cm)^2$

Find the area of the base, multiply it by the height and divide by 3.

anonymous · Answer

i'm sorry i put the wrong question up here

anonymous · Answer

A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. What are the lateral area & surface area of the tea bag?

anonymous · Answer

a. 40 cm^2 ; 52.6 cm^2
b. 40 cm^2 ; 56 cm^2
c. 36.7 cm^2 ; 56 cm^2
d. 36.6 cm^2 ; 52.6 cm^2

anonymous · Answer

do you think you can help with this one

mathstudent55 · Answer

Sure.
Let's draw this new question first.

mathstudent55 · Answer

The slant height of a pyramid is the height of any triangle that is one of the pyramid's lateral faces.

mathstudent55 · Answer

|dw:1437759762207:dw|

mathstudent55 · Answer

The total surface area of the pyramid is the sum of the following two components of the surface area:
1. the area of the base
2. the lateral area, which is the sum of the areas of all lateral faces

Ok so far?

anonymous · Answer

so it would be between a&b?

mathstudent55 · Answer

The area of the base is simply the area of a square of side 4 cm.
The lateral area is the sum of the areas of the 4 congruent triangles that are the sides of the pyramid.
Each triangular face has a base of 4 cm and a height of 5 cm.

mathstudent55 · Answer

Let's find the area of one triangular face:

$A = \dfrac{bh}{2} = \dfrac{(4~cm)(5~cm)}{2} = 10~cm^2$

Each triangular face has an area of 10 cm^2

What is the area of all 4 triangular faces combined?

mathstudent55 · Answer

4 * 10 cm^2 = ?

anonymous · Answer

40cm^;256 cm^2?

anonymous · Answer

did i get it correct?

mathstudent55 · Answer

The area of the sides, the lateral area, is 40 cm^2. That is correct.

mathstudent55 · Answer

What is the area of the base?
It is a square with a 4 cm side.
A = s^2 = (4 cm)^2 = 16 cm^2
The area of the base is 16 cm^2
The total surface area is 40 cm^2 + 16 cm^2 = 56 cm^2
The answer is 
b. 40 cm^2; 56 cm^2