7.5 puzzle time
what do you call a person who makes faces all
day long?
write the letter of each answer in the box containing the exercise number.
find the surface area of the prism.
1. a cube that has side lengths measuring 9 inches
2. a cube that has side lengths measuring 7 inches
3. a rectangular prism that measures 6 inches by 8 inches by 4 inches
4. a rectangular prism that measures 3 inches by 5 inches by 10 inches
5. a rectangular prism that measures 7 inches by 7 inches by 4 inches
6. a rectangular prism that measures 3 inches by 6 inches by 12 inches
7. a rectangular prism that measures 2 inches by 5 inches by 8 inches
8. a triangular prism with bases that are right triangles measuring 5 inches by 12 inches by 13 inches; the height of the prism is 2 inches.
9. a triangular prism with bases that are right triangles measuring 7 inches by 24 inches by 25 inches; the height of the prism is 3 inches.
10. a triangular prism with bases that have a base of 16 inches, legs that are 10 inches, and a height of 6 inches; the height of the prism is 11 inches.
11. a triangular prism with bases that have a base of 18 inches, legs that are 15 inches, and a height of 12 inches; the height of the prism is 7 inches.
answers
m. 190 in²
e. 208 in²
c. 552 in²
l. 210 in²
r. 492 in²
c. 120 in²
k. 132 in²
o. 294 in²
a. 486 in²
a. 336 in²
k. 252 in²

1 8 5 2 11 7 4 9 6 3 10

Question

7.5 puzzle time
what do you call a person who makes faces all
day long?
write the letter of each answer in the box containing the exercise number.
find the surface area of the prism.
1. a cube that has side lengths measuring 9 inches
2. a cube that has side lengths measuring 7 inches
3. a rectangular prism that measures 6 inches by 8 inches by 4 inches
4. a rectangular prism that measures 3 inches by 5 inches by 10 inches
5. a rectangular prism that measures 7 inches by 7 inches by 4 inches
6. a rectangular prism that measures 3 inches by 6 inches by 12 inches
7. a rectangular prism that measures 2 inches by 5 inches by 8 inches
8. a triangular prism with bases that are right triangles measuring 5 inches by 12 inches by 13 inches; the height of the prism is 2 inches.
9. a triangular prism with bases that are right triangles measuring 7 inches by 24 inches by 25 inches; the height of the prism is 3 inches.
10. a triangular prism with bases that have a base of 16 inches, legs that are 10 inches, and a height of 6 inches; the height of the prism is 11 inches.
11. a triangular prism with bases that have a base of 18 inches, legs that are 15 inches, and a height of 12 inches; the height of the prism is 7 inches.
answers
m. 190 in²
e. 208 in²
c. 552 in²
l. 210 in²
r. 492 in²
c. 120 in²
k. 132 in²
o. 294 in²
a. 486 in²
a. 336 in²
k. 252 in²

1  8  5  2  11  7  4  9  6  3  10

Accepted Answer

### Problem 1: Cube with side 9 inches
# Explanation:
## Step1: Recall cube surface area formula
The surface area of a cube is given by $ SA = 6s^2 $, where $ s $ is the side length.
## Step2: Substitute $ s = 9 $
$ SA = 6\times(9)^2 = 6\times81 = 486 $ square inches.
# Answer: A (matches 486 in²)

### Problem 2: Cube with side 7 inches
# Explanation:
## Step1: Use cube surface area formula $ SA = 6s^2 $
## Step2: Substitute $ s = 7 $
$ SA = 6\times(7)^2 = 6\times49 = 294 $ square inches.
# Answer: O (matches 294 in²)

### Problem 3: Rectangular prism (6×8×4)
# Explanation:
## Step1: Recall rectangular prism surface area formula $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 6 $, $ w = 8 $, $ h = 4 $
$ SA = 2((6\times8)+(6\times4)+(8\times4)) = 2(48 + 24 + 32) = 2\times104 = 208 $ square inches.
# Answer: E (matches 208 in²)

### Problem 4: Rectangular prism (3×5×10)
# Explanation:
## Step1: Use $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 3 $, $ w = 5 $, $ h = 10 $
$ SA = 2((3\times5)+(3\times10)+(5\times10)) = 2(15 + 30 + 50) = 2\times95 = 190 $ square inches.
# Answer: M (matches 190 in²)

### Problem 5: Rectangular prism (7×7×4)
# Explanation:
## Step1: Use $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 7 $, $ w = 7 $, $ h = 4 $
$ SA = 2((7\times7)+(7\times4)+(7\times4)) = 2(49 + 28 + 28) = 2\times105 = 210 $ square inches.
# Answer: L (matches 210 in²)

### Problem 6: Rectangular prism (3×6×12)
# Explanation:
## Step1: Use $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 3 $, $ w = 6 $, $ h = 12 $
$ SA = 2((3\times6)+(3\times12)+(6\times12)) = 2(18 + 36 + 72) = 2\times126 = 252 $ square inches.
# Answer: K (matches 252 in²)

### Problem 7: Rectangular prism (2×5×8)
# Explanation:
## Step1: Use $ SA = 2(lw + lh + wh) $
## Step2: Substitute $ l = 2 $, $ w = 5 $, $ h = 8 $
$ SA = 2((2\times5)+(2\times8)+(5\times8)) = 2(10 + 16 + 40) = 2\times66 = 132 $ square inches.
# Answer: K (matches 132 in²)

### Problem 8: Triangular prism (right triangle 5×12×13, height 2)
# Explanation:
## Step1: Recall triangular prism surface area formula: $ SA = 2B + Ph $, where $ B $ is area of base triangle, $ P $ is perimeter of base, $ h $ is height of prism.
## Step2: Calculate $ B $ (area of right triangle): $ \frac{1}{2}\times5\times12 = 30 $
## Step3: Calculate $ P $ (perimeter of triangle): $ 5 + 12 + 13 = 30 $
## Step4: Substitute into formula: $ SA = 2\times30 + 30\times2 = 60 + 60 = 120 $ square inches.
# Answer: C (matches 120 in²)

### Problem 9: Triangular prism (right triangle 7×24×25, height 3)
# Explanation:
## Step1: Use $ SA = 2B + Ph $
## Step2: Calculate $ B $: $ \frac{1}{2}\times7\times24 = 84 $
## Step3: Calculate $ P $: $ 7 + 24 + 25 = 56 $
## Step4: Substitute: $ SA = 2\times84 + 56\times3 = 168 + 168 = 336 $ square inches.
# Answer: A (matches 336 in²)

### Problem 10: Triangular prism (base 16, legs 10, height 6, prism height 11)
# Explanation:
## Step1: First, find area of triangular base $ B = \frac{1}{2}\times16\times6 = 48 $
## Step2: Perimeter of base $ P = 16 + 10 + 10 = 36 $ (assuming isosceles triangle with legs 10)
## Step3: Use $ SA = 2B + Ph $: $ SA = 2\times48 + 36\times11 = 96 + 396 = 492 $ square inches.
# Answer: R (matches 492 in²)

### Problem 11: Triangular prism (base 18, legs 15, height 12, prism height 7)
# Explanation:
## Step1: Calculate $ B $: $ \frac{1}{2}\times18\times12 = 108 $
## Step2: Calculate $ P $: $ 18 + 15 + 15 = 48 $ (isosceles triangle)
## Step3: Use $ SA = 2B + Ph $: $ SA = 2\times108 + 48\times7 = 216 + 336 = 552 $ square inches.
# Answer: C (matches 552 in²)

Now, placing the answers in the boxes (exercise numbers 1,8,5,2,11,7,4,9,6,3,10):

- 1: A
- 8: C
- 5: L
- 2: O
- 11: C
- 7: K
- 4: M
- 9: A
- 6: K
- 3: E
- 10: R

(Note: The shaded box between 1 and 8 is left as is, and the rest are filled with the respective letters. When we arrange the letters according to the box order: 1 (A), [shaded], 8 (C), 5 (L), 2 (O), 11 (C), 7 (K), 4 (M), 9 (A), 6 (K), 3 (E), 10 (R). If we consider the phrase from the puzzle "What Do You Call A Person Who Makes Faces All Day Long", and using the letters: A (1), C (8), L (5), O (2), C (11), K (7), M (4), A (9), K (6), E (3), R (10). Wait, maybe a typo or different arrangement, but the surface area calculations are as above for each problem.)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Cube with side 9 inches

Step1: Recall cube surface area formula

Step2: Substitute \( s = 9 \)

Step1: Use cube surface area formula \( SA = 6s^2 \)

Step2: Substitute \( s = 7 \)

Step1: Recall rectangular prism surface area formula \( SA = 2(lw + lh + wh) \)

Step2: Substitute \( l = 6 \), \( w = 8 \), \( h = 4 \)

Answer:

Problem 2: Cube with side 7 inches