anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Select one: a. 26.7 cm^3 b. 40 cm^3 c. 36.7 cm^3 d. 24.5 cm^3 Incorrect
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
\(\large V_{pyramid} = \dfrac{1}{3}Bh\) 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.

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anonymous
  • anonymous
i'm sorry i put the wrong question up here
anonymous
  • anonymous
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
  • anonymous
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
  • anonymous
do you think you can help with this one
mathstudent55
  • mathstudent55
Sure. Let's draw this new question first.
mathstudent55
  • mathstudent55
The slant height of a pyramid is the height of any triangle that is one of the pyramid's lateral faces.
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
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
  • anonymous
so it would be between a&b?
mathstudent55
  • mathstudent55
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
  • mathstudent55
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
  • mathstudent55
4 * 10 cm^2 = ?
anonymous
  • anonymous
40cm^;256 cm^2?
anonymous
  • anonymous
did i get it correct?
mathstudent55
  • mathstudent55
The area of the sides, the lateral area, is 40 cm^2. That is correct.
mathstudent55
  • mathstudent55
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

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