11.7- Spheres and Hemispheres (Surface area and Volume)

Math Response

Find the volume of the figure. Leave answer in simplified radical form.

V = ... cm³

Type answer here

Correct Answer: 55\sqrt{23}

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Math Response

Find the volume of the figure. Leave answer in terms of $$\pi$$ .

V = ... in³

Type answer here

Correct Answer: 144\pi

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11.7 - Spheres and Hemispheres
Surface Area and Volume

By Gabrielle Quinn

Today we will learn about:

*Volume of spheres & hemispheres

*SA of spheres & hemispheres

SC State Standards:

*G.GGMD.3 - Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems and justify results. Include problems that involve algebraic expressions, composite figures, geometric probability, and real-world applications.

​Surface Area of Hemisphere

Volume of a Sphere

Volume of a Hemisphere

Math Response

Find the Volume of the Sphere.

Leave your answer in terms of $$\pi$$ .

$$V\ =\ ...\ units^3$$

Type answer here

Correct Answer: 288\pi

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Math Response

Find the Surface Area of the Sphere.

Leave your answer in terms of $$\pi$$ .

$$SA\ =\ ...\ units^2$$

Type answer here

Correct Answer: 144\pi

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Math Response

Find the volume of the Hemisphere. Leave answer in terms of $$\pi$$ .

$$V=\ ...\ units^3$$

Type answer here

Correct Answer: 18\pi

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Math Response

Find the Surface Area of the Hemisphere. Leave answer in terms of $$\pi.$$

$$SA\ =\ ...\ units^2$$

Type answer here

Correct Answer: 27\pi

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Open Ended

How could we find the volume of this figure?

Math Response

Find the Volume of the Cylinder first. Leave your answer in terms of $$\pi$$ .

$$V\ =...units^3$$

Type answer here

Correct Answer: 144\pi

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Math Response

Find the Volume of the Hemisphere. Leave your answer in terms of $$\pi$$ and in fraction form.

$$V=...units^3$$

Type answer here

Correct Answer: \frac{128}{3}\pi

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Math Response

Find the Volume of the Cylinder with the hemisphere taken out of the top. Leave your answer in terms of $$\pi$$ and in fraction form. $$V=\ ...cm^3$$

Type answer here

Correct Answer: \frac{304}{3}\pi

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Open Ended

"The area of the base of a hemisphere is $$225\pi\ in^2$$ . What is its volume? "

What do we need in order to find the volume?

Math Response

"The area of the base of a hemisphere is $$225\pi\ in^2$$ . What is its volume? "

If the area of the base is $$225\pi\ in^2$$ . What is the radius?

$$r=...in^{ }$$

Type answer here

Correct Answer: 15

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Math Response

"The area of the base of a hemisphere is $$225\pi\ in^2$$ . What is its volume? "

If the radius is 15 in...now let's find the Volume. Leave answer in terms of $$\pi$$ .

$$V=...in^3$$

Type answer here

Correct Answer: 2250\pi

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Open Ended

What will we need to find the Volume of the figure?

Open Ended

What will we need to find the Surface Area of the Figure?

Math Response

Let's start with Volume of the cone. What is the height of the cone?

$$h=...cm$$

Type answer here

Correct Answer: 3

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Math Response

If the height of the cone is 3cm. What is the Volume of the cone? Leave answer in terms of $$\pi$$ .

$$V=...units^3$$

Type answer here

Correct Answer: 16\pi

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Math Response

Now let's look at the Hemisphere. What is the Volume of the Hemisphere? Leave your answer in terms of $$\pi$$ and in fraction form.

$$V=...units^3$$

Type answer here

Correct Answer: \frac{128}{3}\pi

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Math Response

If the Volume of the Cone = $$16\pi$$

and the

Volume of the Hemisphere = $$\frac{128}{3}\pi$$

What is the Volume of the entire figure? Leave your answer in terms of $$\pi$$ and in fraction form.

$$V=...units^3$$

Type answer here

Correct Answer: \frac{176}{3}\pi

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Math Response

Now let's look at Surface Area. We want to find the Surface Area of the Hemisphere and Cone combined.

What is the Lateral Area of the Cone? Leave your answer in terms of $$\pi$$ .

$$LA=\ ...units^2$$

Type answer here

Correct Answer: 20\pi

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Math Response

Now let's look at Surface Area. We want to find the Surface Area of the Hemisphere and Cone combined.

What is the Lateral Area of the Hemisphere? Leave your answer in terms of $$\pi$$ .

$$LA=\ ...units^2$$

Type answer here

Correct Answer: 32\pi

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Math Response

Now let's look at Surface Area. We want to find the Surface Area of the Hemisphere and Cone combined.

LA cone= 20 $$\pi$$ units²

LA hemisphere= 32 $$\pi$$ units²

What is the Surface Area of the Figure? Leave your answer in terms of $$\pi$$ .

$$SA=\ ...units^2$$

Type answer here

Correct Answer: 52\pi

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Open Ended

If the volume of a sphere is 635 cm³, find its surface area.

If we have the Volume, what will we need to find the Surface Area?

Math Response

If the volume of a sphere is 635 cm³, find its surface area.

What is the radius to the nearest 0.1cm.

$$r=...cm$$

Type answer here

Correct Answer: 5.3

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Math Response

If the radius of the sphere is 5.3 cm. What is the Surface Area?

Round to the nearest tenth (approximate).

$$SA=...cm^2$$

Type answer here

Correct Answer: 353.1

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