8th Grade DCA 4 Corrections

The dimensions of a cylindrical water tank are shown below. Which of the following is the best estimate of the volume of this water tank?

• 58,320 yd³

• 19,440 yd³

• 15,200 yd³

• 1,080 yd³

Answer explanation

To find the volume of a cylindrical tank, use the formula V = πr²h. Given the dimensions, calculating gives approximately 19,440 yd³, making this the best estimate among the options provided.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A conical paper cup is shown in the diagram below. Which value is closest to the maximum volume of water this cup can hold?

• 159 cm³

• 130 cm³

• 40 cm³

• 32 cm³

Answer explanation

To find the volume of a conical cup, use the formula V = (1/3)πr²h. Assuming reasonable dimensions for a small cup, the maximum volume is closest to 40 cm³, making it the correct choice among the options.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A rectangular prism and its dimensions are shown in the diagram. What is the total surface area of this rectangular prism in square inches? Record your answer in the space provided.

Answer explanation

To find the total surface area of a rectangular prism, use the formula: 2(lw + lh + wh). Substitute the dimensions from the diagram into the formula to calculate the total surface area in square inches.

Tags

CCSS.7.G.B.6

A ball shaped like a sphere has a diameter of 5.4 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters?

• 30.54 cm³

• 82.45 cm³

• 122.15 cm³

• 659.58 cm³

Answer explanation

To find the volume of a sphere, use the formula V = (4/3)πr³. The radius r is half the diameter, so r = 2.7 cm. Calculating gives V ≈ 82.45 cm³, which is the closest option.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters?

• 603.19 cm²

• 376.99 cm²

• 245.04 cm²

• 188.50 cm²

Answer explanation

To find the total surface area of a cylinder, use the formula: SA = 2πr(h + r). Here, r = 3 cm (diameter 6 cm), h = 10 cm. Calculating gives SA ≈ 376.99 cm², which is the closest option.

The side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters. The height of the prism is 16.5 meters. What is the lateral surface area of the prism in square meters?

• 23 m²

• 379.5 m²

• 6600 m²

• 126.5 m²

Answer explanation

The lateral surface area of a triangular prism is calculated as the perimeter of the base times the height. The perimeter is 5 + 8 + 10 = 23 meters. Thus, lateral surface area = 23 * 16.5 = 379.5 square meters.

Tags

CCSS.7.G.B.6

Given the dimensions shown below, find the volume of the cone.

• 84.8 in³

• 56.5 in³

• 28.3 in³

• 18.0 in³

Answer explanation

To find the volume of a cone, use the formula V = (1/3)πr²h. Given the dimensions, the calculated volume is approximately 56.5 in³, making it the correct choice.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The radius of a cylinder is 1.25 inches, and the height is 7.5 inches. Which equation can be used to find V, the volume of the cylinder in cubic inches?

• V = π(2.5)²(7.5)

• V = π(7.5)²(2.5)

• V = π(1.25)²(7.5)

• V = π(3.75)²(2.5)

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h. Here, the radius r is 1.25 inches and the height h is 7.5 inches, leading to the equation V = π(1.25)²(7.5), which is the correct choice.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

In each diagram, line g is parallel to line k, and line t intersects lines g and k. Based on the diagrams, the value of x is ______ because the labeled angles in each diagram are corresponding.

• 44°
• 136°

• 42°

• 123°

Answer explanation

The value of x is 136° because the labeled angles in each diagram are corresponding which makes them congruent. Since corresponding angles are equal when lines are parallel, x must be 136.

Tags

CCSS.8.G.A.5

The radius of a cylindrical container of oatmeal is 5 centimeters. The height of the box is 18 centimeters. Which measurement is closest to the lateral surface area of the oatmeal container?

• 1,131 cm²

• 565 cm²

• 283 cm²

• 90 cm²

Answer explanation

The lateral surface area of a cylinder is calculated using the formula: 2πrh. Here, r = 5 cm and h = 18 cm. Thus, the lateral surface area = 2 × π × 5 × 18 ≈ 565 cm², making 565 cm² the closest measurement.