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.

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.

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.

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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.

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.

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.

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.

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.

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.

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.