Question

3. John made a regular quadrilateral pyramid out of wood, with a base side of 32 cm and a side wall height of 20 cm. 1) Calculate the total surface area of the pyramid. 2) How many grams of paint are needed to paint this pyramid if 0.2 kg of paint is needed per m2? Give your answer to the nearest 1 g.

Answer 1

`\begin{gathered} a)\text{ 2,304 cm}^2 \\ b)\text{ 460,800 g} \end{gathered}`

Step-by-step explanation:

a) We want to calculate the total surface area of the pyramid

Mathematically, we have that as:

`A\text{ = }(1)/(2)Pl\text{ + B}`

P is the perimeter of base = 4 * 32 = 128 cm

l is the slant height = 20 cm

B is the base area which is 32 * 32 = 1024 cm^2

The surface area is thus:

`\begin{gathered} (1)/(2)*128*20\text{ + 1024 = 1280 + 1024 = 2,304 cm}^2 \\ \end{gathered}`

b) To get the mass needed, we multiply the total surface area by the kg/m^2

We have that as:

`\begin{gathered} 2304\text{ }*\text{ 0.2 = 460.8 kg} \\ To\text{ g, we multiply by 1000} \\ 460.8\text{ }*\text{ 1000 = 460,800 g} \end{gathered}`