Volume of cylinder, cones and spheres (8.G.9)

Imagine Raneisha, Aiden, and Sierra are teaming up for an exciting environmental project. They've decided to construct a large cylindrical rainwater collector to study sustainable water collection methods! But, oh no! They need to figure out how much rainwater it can collect. Can you help them choose the right formula to calculate the volume of their collector?

• V = πrh

• V = 2πr^2h

• V = πr^2h

• V = πr^3

Answer explanation

The correct formula to calculate the volume of a cylinder is V = πr^2h, where r is the radius and h is the height of the cylinder.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Imagine Asia, Raneisha, and Cyonnia are teaming up for a school science project. They've decided to build an innovative cylindrical rainwater collector. If this unique collector has a radius of 5 cm and a height of 10 cm, can you help them calculate the volume of their creation?

• 200π cm^3

• 300π cm^3

• 150π cm^3

• 250π cm^3

Answer explanation

The volume of a cylinder is calculated using the formula V = πr^2h. Substituting r = 5 cm and h = 10 cm, V = π(5^2)(10) = 250π cm^3. Therefore, the correct answer is 250π cm^3.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Sierra, Raneisha, and Cyonnia are working together on an environmental project to create an innovative, cone-shaped rain gauge. They're exploring the mathematics behind it to ensure it can accurately measure rainfall. Which magical formula should they use to calculate the volume of rainwater their gauge can collect?

• (1/3) * π * r^2 * h

• π * r * h

• 2 * π * r * h

• (1/2) * π * r^2 * h

Answer explanation

The correct formula to calculate the volume of a cone is (1/3) * π * r^2 * h.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Jakari, Sierra, and Asia are collaborating on a science project to construct an innovative, cone-shaped bird feeder for their biology class. They've determined the radius of their bird feeder will be 4 cm and the height an impressive 6 cm. Can you assist them in calculating the volume of their bird feeder creation?

• 40π cm^3

• 16π cm^3

• 32π cm^3

• 24π cm^3

Answer explanation

The volume of a cone is calculated using the formula V = (1/3)πr^2h. Substituting r=4 cm and h=6 cm, V = (1/3)π(4^2)(6) = 32π cm^3.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Imagine Rylee, Kaiyah, and Reginald are building a magical snow globe together. They're curious to find out how much glittery liquid they can pour into their spherical globe to make it sparkle. Can you help them figure out the right formula to calculate the volume of their globe?

• 2 * π * r^3

• π * r^2

• (4/3) * π * r^3

• (4/3) * π * r^2

Answer explanation

The correct formula to calculate the volume of a sphere is (4/3) * π * r^3, where r is the radius of the sphere.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Ahmaad and Rome are working on a science project in their backyard when they discover a perfectly round basketball. Cyonnia, who is a math enthusiast, tells them that the basketball has a radius of 3 cm. Can you help them figure out the volume of this basketball?

• 27π cm³

• 36π cm³

• 9π cm³

• 45π cm³

Answer explanation

The volume of a sphere is calculated using the formula V = (4/3)πr^3. Substituting r=3, V = (4/3)π(3)^3 = 36π cm^3.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Imagine Rylee, Asia, and Rome are having a fun challenge packing books into a rectangular box for their community library. Can you help them figure out the secret formula to calculate the volume of this box?

• V = l * w * h

• V = l - w - h

• V = l / w / h

• V = l + w + h

Answer explanation

The correct formula to calculate the volume of a rectangular prism is V = l * w * h, where l is the length, w is the width, and h is the height.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Kaiyah, Raneisha, and Cyonnia are setting up a booth for their school fair! They've found a special box that is 8 cm long, 4 cm wide, and 6 cm high. Can you help them figure out the volume of this unique box?

• 192 cubic cm

• 48 cubic cm

• 36 cubic cm

• 112 cubic cm

Answer explanation

To find the volume of a rectangular prism, multiply the length, width, and height together: 8 cm * 4 cm * 6 cm = 192 cubic cm. Therefore, the correct answer is 192 cubic cm.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Imagine Asia, Aiden, and Kaniya are tasked with a project in their history class to construct the most accurate model of an Egyptian pyramid. Asia is excited but a bit confused about how to calculate the volume of her pyramid model. Can you help her figure out which formula to use?

• 2 * base area * height

• (1/3) * base area * height

• base area * height

• (1/2) * base area * height

Answer explanation

The correct formula to calculate the volume of a pyramid is (1/3) * base area * height.

Tags

CCSS.HSG.GMD.A.3

Imagine Aiden, D'Ajjah, and Tameiera are teaming up for a thrilling school project: constructing a model pyramid! They've meticulously calculated the base area to be 20 sq. units and have decided the pyramid will stand tall at 12 units. Can you help them figure out the volume of their magnificent pyramid?

• 240

• 50

• 80

• 100

Answer explanation

To find the volume of a pyramid, use the formula V = (1/3) * base area * height. Substituting the values, V = (1/3) * 20 * 12 = 80. Therefore, the volume of the pyramid is 80.

Tags

CCSS.HSG.GMD.A.3