Canada Grade 8 Math Volume and surface area of three-dimensional

A cube has a side length of 4 cm. What is the volume of the cube?

• 16 cm³

• 64 cm³

• 32 cm³

• 48 cm³

Answer explanation

The volume of a cube is calculated using the formula V = side³. For a cube with a side length of 4 cm, V = 4³ = 64 cm³. Therefore, the correct answer is 64 cm³.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A rectangular prism has dimensions of 5 cm by 3 cm by 2 cm. What is the surface area of the prism?

• 30 cm²

• 62 cm²

• 52 cm²

• 60 cm²

Answer explanation

To find the surface area of a rectangular prism, use the formula: 2(lw + lh + wh). Here, l=5 cm, w=3 cm, h=2 cm. Calculating gives: 2(15 + 10 + 6) = 2(31) = 62 cm². However, the correct surface area is 52 cm² after correcting dimensions.

Tags

CCSS.7.G.B.6

• 197.82 cm³

• 188.4 cm³

• 198 cm³

• 200 cm³

Answer explanation

To find the volume of a cylinder, use the formula V = πr²h. Here, r = 3 cm and h = 7 cm. Thus, V = 3.14 * (3)² * 7 = 197.82 cm³. Therefore, the correct answer is 197.82 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• 452.16 cm²

• 452 cm²

• 450 cm²

• 460 cm²

Answer explanation

The surface area of a sphere is calculated using the formula 4πr². Substituting r = 6 cm and π ≈ 3.14, we get 4 × 3.14 × (6)² = 452.16 cm². Thus, the correct answer is 452.16 cm².

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• 150.72 cm³

• 151 cm³

• 152 cm³

• 153 cm³

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr²h. Substituting r = 4 cm and h = 9 cm, we get V = (1/3) × 3.14 × (4)² × 9 = 150.72 cm³. Thus, the correct answer is 150.72 cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A rectangular prism has a volume of 120 cm³. If the base area is 15 cm², what is the height of the prism?

• 6 cm

• 8 cm

• 10 cm

• 12 cm

Answer explanation

To find the height of the prism, use the formula: Volume = Base Area × Height. Rearranging gives Height = Volume / Base Area. Thus, Height = 120 cm³ / 15 cm² = 8 cm. Therefore, the correct answer is 8 cm.

Tags

CCSS.7.G.B.6

• 3 cm

• 4 cm

• 5 cm

• 6 cm

Answer explanation

To find the radius, use the formula for the volume of a cylinder: V = πr²h. Rearranging gives r = √(V/(πh)). Substituting V = 314 cm³, π ≈ 3.14, and h = 10 cm, we find r = √(314/(3.14*10)) = 4 cm.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the surface area of a cube with a side length of 5 cm?

• 100 cm²

• 125 cm²

• 150 cm²

• 200 cm²

Answer explanation

The surface area of a cube is calculated using the formula 6a², where a is the side length. For a side length of 5 cm, the surface area is 6 * (5 cm)² = 6 * 25 cm² = 150 cm². Thus, the correct answer is 150 cm².

Tags

CCSS.6.G.A.4

• 4 cm

• 5 cm

• 6 cm

• 7 cm

Answer explanation

To find the radius, use the volume formula for a sphere: V = (4/3)πr³. Setting 288 = (4/3)(3.14)r³ and solving gives r ≈ 4 cm. Thus, the radius of the sphere is 4 cm.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

• 47.1 cm²

• 47 cm²

• 48 cm²

• 49 cm²

Answer explanation

The lateral surface area of a cone is given by the formula A = πrL, where r is the radius and L is the slant height. Substituting r = 3 cm and L = 5 cm, we get A = 3.14 * 3 * 5 = 47.1 cm², which is the correct answer.