Surface Area of 3D Shapes Quiz

What is the total surface area formula for a prism? 

• S = 2πrh +2πr²

• S = Ph + 2B

• S = πrl + πr²

• S = ½Pl + B

Answer explanation

The total surface area of a prism is calculated using the formula S = Ph + 2B, where P is the perimeter of the base, h is the height, and B is the area of the base. This formula accounts for both the lateral area and the two bases.

What is the lateral surface area formula for a prism? 

• S = 2πrh +2πr²

• S = Ph

• S = πrl + πr²

• S = Ph + 2B

Answer explanation

The lateral surface area of a prism is calculated using the formula S = Ph, where P is the perimeter of the base and h is the height. This formula accounts for the area of the sides, excluding the bases.

What is the difference between lateral and total surface area of a cylinder?

• Lateral surface area includes the bases, total does not.

• Total surface area includes the bases, lateral does not.

• They are the same.

• Lateral surface area is always greater than total surface area.

Answer explanation

The total surface area of a cylinder includes the areas of the two circular bases, while the lateral surface area only accounts for the curved surface between the bases. Therefore, total surface area includes the bases, lateral does not.

• The height of the prism

• The perimeter of the base

• The area of the base

• The volume of the prism

• The height of the base triangle

• The height of the prism itself

• The height of the lateral face

• The height of the entire structure

Answer explanation

The correct height for calculating the surface area of a prism is the height of the prism itself, as it represents the vertical extent of the solid, affecting the area of the lateral faces and overall surface area.

• The height of the prism

• The perimeter of the base

• The area of the base

• The volume of the prism

Answer explanation

In the context of a prism, the symbol B typically represents the area of the base. This is crucial for calculating the volume, as the volume is found by multiplying the area of the base (B) by the height (h) of the prism.

What is the surface area formula for a cylinder? 

• S = 2πrh +2πr²

• S = Ph + 2B

• S = πrl + πr²

• S = ½Pl + B

Answer explanation

The surface area formula for a cylinder is S = 2πrh + 2πr², where r is the radius and h is the height. This formula accounts for the lateral area (2πrh) and the area of the two circular bases (2πr²).

Tags

CCSS.7.G.B.6

Answer explanation

The radius of a cylinder is half of its diameter. Given the diameter is 10 cm, the radius is 10 cm ÷ 2 = 5 cm. Therefore, the correct answer is 5 cm.

Answer explanation

The total surface area of a cylinder is given by the formula \(2\pi r(h + r)\). Substituting \(r = 2\, \text{cm}\) and \(h = 10\, \text{cm}\), we get \(2\pi(2)(10 + 2) = 48\pi\, \text{cm}^2\). Thus, the correct answer is \(48\pi\, \text{cm}^2\).

Answer explanation

The lateral surface area of a cylinder is given by the formula A = 2πrh. Here, r = d/2 = 3 cm and h = 8 cm. Thus, A = 2π(3)(8) = 48π cm². Therefore, the correct answer is 48π cm².