McGraw Hill Math Grade 7 Lesson 26.5 Answer Key Surface Area of Solid Figures

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McGraw-Hill Math Grade 7 Answer Key Lesson 26.5 Surface Area of Solid Figures

Exercises

CALCULATE SURFACE AREA

Question 1.

Answer:
SA = 54 sq in.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 3 x 3 + 2 x 3 x 3 + 2 x 3 x 3
SA = 18 + 18 + 18
SA = 54 sq in.

Question 2.

Answer:
SA = 104 sq m.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 6 x 5 + 2 x 5 x 2 + 2 x 2 x 6
SA = 60 + 20 + 24
SA = 104 sq in
Question 3.

Answer:
SA = 450.325 sq in.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 7.25 x 10 + 2 x 10 x 8.85 + 2 x 8.85 x 7.25
SA = 145 + 177 + 128.325
SA = 450.325 sq in

Question 4.

Answer:
SA = 125.46 sq ft.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 4.2 x 1.5 + 2 x 1.5 x 9.9 + 2 x 9.9 x 4.2
SA = 12.6 + 29.7 + 83.16
SA = 125.46 sq ft.

Question 5.

Answer:
SA = 856 sq cm.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 10 x 12 + 2 x 12 x 14 + 2 x 14 x 10
SA = 240 + 336 + 280
SA = 856 sq cm.
Question 6.

Answer:
SA = 862 sq m.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 11 x 12 + 2 x 12 x 13 + 2 x 13 x 11
SA = 264 + 312 + 286
SA = 862 sq m.

Question 7.

Answer:
SA = 478 sq m.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 9 x 7 + 2 x 7 x 11 + 2 x 11 x 9
SA = 126 + 154 + 198
SA = 478 sq m

Question 8.

Answer:
SA = 114 sq in.

Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 8 x 3 + 2 x 3 x 3 + 2 x 3 x 8
SA = 48 + 18 + 48
SA = 114 sq in

Question 9.

Answer:
SA = 370 sq ft.
Explanation:
The surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area.
SA = 2 l w + 2 l h + 2 h w
SA = 2 x 5 x 25 + 2 x 25 x 2 + 2 x 2 x 5
SA = 250 + 100 + 20
SA = 370 sq ft

Keep your answer in a form of pi.

Question 10.

Answer:
SA = 60π sq cm.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 3 (7 + 3)
SA = 60π sq. units

Question 11.

Answer:
SA = 170π sq in.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 5( 12 + 5)
SA = 170π sq in.

Question 12.

Answer:
SA = 252π sq in.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 9 ( 5 + 9)
SA = 252π sq in.

Question 13.

Answer:
SA = 275π sq m.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x11(1.5 + 11)
SA = 275π sq m.

Question 14.

Answer:
SA = 96.3π sq ft.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 4.5(6.2 + 4.5)
SA = 96.3π sq ft.

Question 15.

Answer:
SA = 352π sq in.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 8(14+ 8)
SA = 352π sq in.

Question 16.

Answer:
SA = 84π sq cm.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 6( 1 + 6)
SA = 84π sq cm.

Question 17.

Answer:
SA = 138.125π sq in.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x 4.25 (12 + 4.25)
SA = 138.125π sq in.

Question 18.

Answer:
SA = 600π sq in.
Explanation:
surface area of cylinder = Area of curved surface + Area of two circular regions
= CSA of cylinder + πr² + πr²
= 2πrh + 2πr²
Therefore, Total surface area of cylinder = 2πr (h + r) sq. units
Where r is the radius of the base and h is the height of the cylinder.
SA of cylinder = 2πr (h + r) sq. units
SA = 2π x10 (20 + 10)
SA = 600π sq in.