The image presents an exercise labeled as "8)" with the following instruction:**"Calculate the surface area and volume of the figure shown below:"**The accompanying diagram depicts a 3D solid with the following dimensions:- The height of the trapezoidal face is labeled as 10 feet.- The top side of the trapezoid is 8 feet.- The bottom side of the trapezoid measures 12 feet.- The depth (the length of the solid along the direction perpendicular to the trapezoidal face) is 35 feet.- The inclined side of the trapezoid measures 10 feet.- The slanted or lateral height from the top of the trapezoidal face to the base is 12 feet.- The vertical side of the rectangle at the end is 25 feet.The figure appears to be a prism with a trapezoidal base extending into the third dimension. The task is to find both the total surface area and the volume of the prism.

area of trapezium=12(b1+b2)×h=12(8+25)×8=132 sqr ftbelow trapezium rectangular fig whose area can…

Answered: 8) Calculate the surface area and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The image presents an exercise labeled as "8)" with the following instruction:

**"Calculate the surface area and volume of the figure shown below:"**

The accompanying diagram depicts a 3D solid with the following dimensions:

- The height of the trapezoidal face is labeled as 10 feet.
- The top side of the trapezoid is 8 feet.
- The bottom side of the trapezoid measures 12 feet.
- The depth (the length of the solid along the direction perpendicular to the trapezoidal face) is 35 feet.
- The inclined side of the trapezoid measures 10 feet.
- The slanted or lateral height from the top of the trapezoidal face to the base is 12 feet.
- The vertical side of the rectangle at the end is 25 feet.

The figure appears to be a prism with a trapezoidal base extending into the third dimension. The task is to find both the total surface area and the volume of the prism.

Expert Solution

Step 1

$a r e a o f t r a p e z i u m = \frac{1}{2} (b_{1} + b_{2}) \times h = \frac{1}{2} (8 + 25) \times 8 = 132 s q r f t b e l o w t r a p e z i u m r e c \tan g u l a r f i g w h o s e a r e a c a n b e f i n d b y L \times B = 12 \times 25 = 300 s q r f t a r e a o f t h r e e r e c \tan g u l a r s h a p e o n c u r v e d p a r t = 8 \times 35 + 10 \times 35 + 12 \times 35 = 1050 s q r f t t o t a l a r e a o f f i g s h o w i s 1050 + 300 + 132 = 1482 s q r f t t o t a l a r e a f r o n t a n d b a c k = 2 \times 1482 = 2964 s q r f t$

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