Let's go through the responses to each of the questions based on the shapes and calculations involved.
Question 2:
Which of these everyday objects has the attributes of a right rectangular prism?
- The objects that are typically right rectangular prisms include boxes, books, and other rectangular solids.
Question 3:
What type of pyramids are the Pyramids of Giza? Describe the attributes.
- They are square pyramids. They have 5 faces (the 4 lateral faces are triangles, and the 5th face is a square base). Each pyramid has 5 vertices, 8 edges, and the 4 lateral faces meet at a single point (the apex).
Correct Response:
They are square pyramids. They have 5 faces. The 4 lateral faces are triangles, and the 5th face is a square base. Each pyramid has 5 vertices and 8 edges. The 4 lateral faces meet at a single point, or apex.
Question 4:
What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?
- The surface area \(SA\) of a right rectangular prism is given by the formula: \[ SA = 2(lw + lh + wh) \] If all edges are 15.10 cm, that means \(l = w = h = 15.10\): \[ SA = 2(15.10 \cdot 15.10 + 15.10 \cdot 15.10 + 15.10 \cdot 15.10) \] \[ SA = 2(3 \cdot 15.10^2) = 6 \cdot 15.10^2 \] Calculating \(15.10^2\): \[ 15.10^2 = 228.01 \] Thus: \[ SA = 6 \cdot 228.01 = 1368.06 , cm^2 \]
Correct Response:
1,368.06 cm²
Question 5:
What is the surface area of a carry-on suitcase measuring 9.5 inches long, 16 inches wide, and 22.5 inches high?
- The surface area \(SA\) is calculated as: \[ SA = 2(lw + lh + wh) \] Calculating this: \[ SA = 2(9.5 \times 16 + 9.5 \times 22.5 + 16 \times 22.5) \] Calculating each term:
- \(9.5 \times 16 = 152\)
- \(9.5 \times 22.5 = 213.75\)
- \(16 \times 22.5 = 360\)
So, \[ SA = 2(152 + 213.75 + 360) = 2(725.75) = 1451.5 , in^2 \]
Correct Response:
1,451.5 in²
Question 6:
Surface area of rectangular pyramid with l = 15 m, w = 12 m, and h = 10 m:
- The surface area is calculated as follows: \[ SA = lw + \frac{1}{2} \cdot (l + w) \cdot slant , height \] Assuming we need to calculate the slant height using the Pythagorean theorem (not provided):
- Find the slant height with known h using equations derived from the dimensions.
- Plug in the values of l, w, and the calculated slant height.
Question 7:
Surface area of a square pyramid with base edge 1.5 cm and slant height 4 cm:
- The surface area \(SA\) is given by: \[ SA = b^2 + 2 \cdot \frac{1}{2} \cdot b \cdot slant , height \] Where \(b = 1.5\): \[ = 1.5^2 + 2 \cdot \frac{1}{2} \cdot 1.5 \cdot 4 = 2.25 + 12 = 14.25 , cm^2 \]
Question 8:
Height of the base in a triangular pyramid:
- For the height calculation, we'd typically use properties of right triangles again. The area and dimensions supplied in earlier parts of the question would be plugged into the area formula for triangles.
Question 9:
Surface area for triangular pyramids for the dome on the fence project. Calculates by applying the pyramid area formulas as mentioned earlier.
Question 10:
Length of a right rectangular prism (Volume = 90, Width = 3, Height = 5):
- Using \(Volume = length \cdot width \cdot height\): \[ 90 = length \cdot 3 \cdot 5 \rightarrow length = \frac{90}{15} = 6 \]
Question 11:
Volume of a right rectangular prism with area of 20 square units and height of 3 units:
- Volume = base area × height: \[ V = 20 \cdot 3 = 60 , units^3 \]
Question 12:
Volume of gift box (base = 15 in², height = 5 in):
- Volume = base area × height: \[ V = 15 \cdot 5 = 75 , in^3 \]
Question 13:
Volume of rectangular pyramid with dimensions 32 cm, 25 cm, height 41 cm:
- Volume = \(\frac{1}{3} \cdot base , area \cdot height\): \[ Volume = \frac{1}{3} \cdot (32 \cdot 25) \cdot 41 = \frac{1}{3} \cdot 800 \cdot 41 = \frac{32800}{3} \approx 10933.33 , cm^3 \]
Question 14:
Volume of an upside-down pyramid (50 ft by 20 ft, depth 25 ft): Using the volume formula for a rectangular pyramid: \[ V = \frac{1}{3} \cdot base , area \cdot height \] Thus: \[ V = \frac{1}{3} \cdot (50 \cdot 20) \cdot 25 = \frac{1}{3} \cdot 1000 \cdot 25 = \frac{25000}{3} \approx 25000 , ft^3 \]
Feel free to follow up for any specific calculations or additional questions!
1 answer