Question

1. mp reasoning a hanging light cover made of glass is shaped like a square pyramid. the cover does not have a bottom. one square foot of the glass weighs 2.45 pounds. the chain can support 35 pounds. will the chain support the light cover? explain.

Explanation:

Step1: Find the lateral surface area of the square pyramid

A square pyramid has 4 triangular faces. The base of each triangle is 2 ft (since the base of the square is 2 ft) and the slant height is 2.5 ft. The area of a triangle is $\frac{1}{2} \times base \times height$. So the area of one triangular face is $\frac{1}{2} \times 2 \times 2.5 = 2.5$ square feet. For 4 faces, the lateral surface area $LSA = 4 \times 2.5 = 10$ square feet.

Step2: Calculate the weight of the glass

One square foot of glass weighs 2.45 pounds. So the weight of 10 square feet of glass is $10 \times 2.45 = 24.5$ pounds.

Step3: Compare the weight with the chain's capacity

The chain can support 35 pounds. Since $24.5 < 35$, the chain can support the light cover.

Answer:

Yes, the chain will support the light cover. The lateral surface area of the square - pyramid - shaped light cover is 10 square feet. The weight of the glass is $10\times2.45 = 24.5$ pounds, and since $24.5$ pounds is less than the 35 - pound capacity of the chain, the chain can support the light cover.