question 8\nenergy a british thermal unit (btu) is equal to the amount of energy used to raise the…

question 8\nenergy a british thermal unit (btu) is equal to the amount of energy used to raise the temperature of one pound of water 1°f. a house is shaped like a rectangular prism with a length, width, and height of 80 feet, 25 feet, and 8 feet, respectively. approximately 60,000 btus are required to heat the house properly.\na. what is the density of the house in btus?\nbtus/ft³\nb. a nearby house requires approximately 52,000 btus for heating. if the house is 31 feet long and 25 feet wide, what is the height of the house? round your answer to the nearest foot.\nft

question 8\nenergy a british thermal unit (btu) is equal to the amount of energy used to raise the temperature of one pound of water 1°f. a house is shaped like a rectangular prism with a length, width, and height of 80 feet, 25 feet, and 8 feet, respectively. approximately 60,000 btus are required to heat the house properly.\na. what is the density of the house in btus?\nbtus/ft³\nb. a nearby house requires approximately 52,000 btus for heating. if the house is 31 feet long and 25 feet wide, what is the height of the house? round your answer to the nearest foot.\nft

Answer

Explanation:

Step1: Calculate volume of first house

The volume $V$ of a rectangular prism is $V = l\times w\times h$. For the first house, $l = 80$ ft, $w = 25$ ft, $h = 8$ ft. So $V_1=80\times25\times8=16000$ $ft^3$.

Step2: Calculate density of first house

Density $D$ is the amount of energy per unit volume. Given energy $E_1 = 60000$ BTUs and $V_1 = 16000$ $ft^3$. Then $D=\frac{E_1}{V_1}=\frac{60000}{16000}= 3.75$ BTUs/$ft^3$.

Step3: Calculate volume of second house

Let the height of the second house be $h_2$. The volume $V_2=l_2\times w_2\times h_2$, where $l_2 = 31$ ft and $w_2 = 25$ ft. So $V_2=31\times25\times h_2 = 775h_2$ $ft^3$.

Step4: Calculate height of second house

We know the density is the same for similar - heating situations. Since density $D = 3.75$ BTUs/$ft^3$ and energy $E_2 = 52000$ BTUs, and $D=\frac{E_2}{V_2}$. Then $V_2=\frac{E_2}{D}=\frac{52000}{3.75}\approx13866.67$ $ft^3$. Also, $V_2 = 775h_2$. So $h_2=\frac{V_2}{775}=\frac{13866.67}{775}\approx18$ ft.

Answer:

a. $3.75$ b. $18$