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## Texas Go Math Grade 8 Module 10 Quiz Answer Key

**Texas Go Math Grade 8 Module 10 Ready to Go On? Answer Key**

**10.1 Surface Area of Prisms**

**Find the lateral and total surface area of each prism. Round your answers to the nearest tenth if necessary.**

Question 1.

Answer:

Given that the prism is a rectangular prism.

Lateral surface area of a rectangular prism = 2(l + w)h.

Length = l = 18cm

Width = w = 10cm

Height = h = 6cm.

=2(18 + 10)6.

=2(28)6.

= 336 square units.

Question 2.

Answer:

Given that the prism is the triangular prism.

The formula for the lateral surface of the triangular prism = perimeter of the base x height of the prism = (a + b + c)h.

H = 8yd

A = 25yd

B = 10yd

C = 6yd

= (25 + 10 + 6)8

= (41)8

= 328yd.

The lateral surface area of the triangular prism = 328 yd²

328 rounded to the nearest ten is 330. Because in the 336 the one’s place is greater than the 5. Thus replace 0 by 0 and tens place by 3.

Question 3.

Answer:

Given that the prism is the triangular prism.

The formula for the lateral surface of the triangular prism = perimeter of the base x height of the prism = (a + b + c)h.

H = 15m

A = 17m

B = 13m

C = 16m

= (17 + 13 + 16)15

= (46)15

= 690m.

The lateral surface of the triangular prism = 690m²

690 rounded to the nearest ten is 690.

Question 4.

Answer:

Given that the prism is a rectangular prism.

Lateral surface area of a rectangular prism = 2(l + w)h.

Length = l = 14.5mm

Width = w = 10mm

Height = h = 4.2mm

=2(14.5 + 10)4.2.

=2(24.5)4.2.

= 205.8mm²

205.8 rounded to the nearest ten is 205. Because in the 205.8 the decimal place is greater than the 5. So replace the 8 by 0

**10.2 Surface Area of Cylinders**

**Find the lateral and total surface area of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.**

Question 5.

Answer:

Formula for the lateral surface area of the cylinder is 2πRH.

Diameter = 18yd

Radius = 18/2 = 9

H = height = 14yd

R = radius = 9yd

LA = 2 x 3.14 x 9 x 14.

lateral surface area of the cylinder= 791.28yd.

791.28 is rounded to the nearest tenth is 791.20. Because in the decimal the one’s place is greater than 5 so it is replaced by 0.

Question 6.

Answer:

The formula for the lateral surface area of the cylinder is 2πRH.

H = height = 9ft

R = radius = 7ft

LA = 2 x 3.14 x 7 x 9.

the lateral surface area of the cylinder= 395.64ft

395.64 is rounded to the nearest tenth is 1582.60. Because in the decimal the one’s place is less than 5 so it is replaced by 0.

**Essential Question**

Question 7.

How can finding surface area help you solve packaging problems?

Answer: The packaging boxes are in the shape of a cuboid and it has 6 faces. Its label has length, width, and height. The surface area of the prism is SA = 2lw + 2lh + 2hw.

**Texas Go Math Grade 8 Module 10 Mixed Review Texas Test Prep Answer Key**

**Selected Response**

Question 1.

Grain is stored in cylindrical structures called silos. Which is the best estimate for the volume of a silo with a diameter of 12.3 feet and a height of 25 feet?

(A) 450 cubic feet

(B) 900 cubic feet

(C) 2970 cubic feet

(D) 10,800 cubic feet

Answer:

The formula for the volume of the cylinder = 2πr2h.

H = 25feet

Diameter = 12.3 feet

Radius = d/2 = 12.3/2 =6.15.

= 2 x 3.14 x (12.3)2 x 25

= 2969.06625 = 2970 cubic feet.

Option C is the correct answer.

Question 2.

What is the side length of a cube that has a total surface area of 384 square inches?

(A) 6 inches

(B) 7 inches

(C) 8 inches

(D) 9 inches

Answer:

Given that total surface area of the cube = 384 inches

Formula for the total surface area = 6a²

= 6(6)² = 216 inches.

= 6(7)² = 294 inches.

= 6(8)² = 384 inches.

= 6(9)² = 486 inches.

Option C is the correct answer.

Question 3.

A block of cheese is shown in the shape of the triangular prism below.

What is the total surface area of the block of cheese?

(A) 120 in^{2}

(B) 494 in^{2}

(C) 510 in^{2}

(D) 640 in^{2}

Answer:

There are two triangles in the triangular prism

Area of the one triangle = ½ x b x h

= ½ x 17 x 15 = 127.5

Area of the two triangle = ½ x b x h

= 1/2 x 8 x 13 = 52

The formula for the total surface area of the triangle = area of one triangle + area of two triangles.

= 179.5 square inches.

Question 4.

Using 3.14 for π, what is the lateral surface area of the cylinder to the nearest unit?

(A) 122 yd^{2}

(B) 204 yd^{2}

(C) 383 yd^{2}

(D) 587 yd^{2}

Answer:

The formula for the lateral surface area of the cylinder is 2πRH.

Diameter = 11.4yd

Radius = 11.4/2 = 5.7yd

H = height = 10.7yd

R = radius = 5.7yd

LA = 2 x 3.14 x 5.7 x 10.7.

the lateral surface area of the cylinder= 383.01yd^{2}

383.01 is rounded to the nearest tenth of 383. Because in the decimal the one’s place is less than 5 so it is replaced by 0.

Option C is the correct answer.

Question 5.

The net of a cylinder is shown.

What is the total surface area of the cylinder represented by the net?

(A) 1607.7 m^{2}

(B) 1856 m^{2}

(C) 4220.2 m^{2}

(D) 5827.8 m^{2}

Answer:

The formula for the surface area of the cylinder = 2πr(r + h).

H = 42m

Diameter = 32m

Radius = 32/2 = 16m

= 2 x 3.14 x 16(16 + 42)

= 100.48(58)

= 5827.8

Option D is the correct answer.

Question 6.

A cylinder has a circumference of 12π cm and a height that is half the radius. What is the total surface area of the cylinder?

(A) 367π cm^{2}

(B) 72π cm^{2}

(C) 108π cm^{2}

(D) 144π cm^{2}

Answer:

The formula for the surface area of the cylinder = 2πr(r + h).

Circumference = 12π/π

= 12 is the diameter.

Radius = d/2 = 12/2 = 6

R = 6

H = half the radius = 6/2 = 3.

= 2 x π x 6(6 + 3)

= 6.28 x 54

= 108πcm²

Option C is the correct answer.

**Gridded Response**

Question 7.

A rectangular prism has a length of 4 feet, a width of 1 yard, and a height of 3 inches. What is the total surface area of the prism to the nearest tenth of a square foot?

Answer:

Formula for the surface area of the rectangular prism = 2(lb + bh + lh).

L = 4 feet.

1 feet 12 inches

4 feets = 12 x 4 = 48 inches.

Width = breadth = B = 1 yard.

1 yard = 36 inches.

H = 3 inches.

= 2(48 x 36 + 36 x 3 + 48 x 3)

= 2(1728 + 108 + 144)

= 3960 inches = 27.5 square foot

27.5 nearest tenth to square foot is 27.5