We read your photo as:

A hollow square base container has two identical spherical balls in it that fit exactly in the tube so that each ball is in contact with the other ball and the five faces of walls of the container. The square has a length of 10cm.

Mathematics

ScanSolve AI Answer

Answers

4 parts
6.1

20 cm20 \text{ cm}

6.2

2000 cm32000 \text{ cm}^3

6.3

1047.20 cm31047.20 \text{ cm}^3

6.4

952.80 mL952.80 \text{ mL}

Step-by-step solution

8 steps

Here's the solution for Question 6:

Part 6.1· 2 steps

Calculate height of the container.

The problem states that the two identical spherical balls fit exactly in the container, and each ball is in contact with the other ball and the five faces of the container walls. The square base has a length of 10 cm.
Since the balls fit exactly in the square base, the diameter of each sphere must be equal to the side length of the square base.
Diameter of one sphere = 10 cm.
Since there are two identical spheres stacked on top of each other, the total height they occupy is twice the diameter of one sphere.
The container's height must be equal to this total height.

  1. Determine the diameter of one sphere.

    Diameter of sphere=Side length of square base=10 cm\text{Diameter of sphere} = \text{Side length of square base} = 10 \text{ cm}

  2. Calculate the height of the container.

    Height of container=2×Diameter of sphere\text{Height of container} = 2 \times \text{Diameter of sphere} Height of container=2×10 cm\text{Height of container} = 2 \times 10 \text{ cm} Height of container=20 cm\text{Height of container} = \boxed{20 \text{ cm}}

Part 6.2

2000 cm32000 \text{ cm}^3

Calculate the volume of the container.

The container is a square prism (or cuboid) with a square base of side length 10 cm and a height of 20 cm (from 6.1).
The formula for the volume of a prism is V=Base Area×HeightV = \text{Base Area} \times \text{Height}.

  1. Calculate the base area.

    Base Area=(Side length)2=(10 cm)2=100 cm2\text{Base Area} = (\text{Side length})^2 = (10 \text{ cm})^2 = 100 \text{ cm}^2

  2. Calculate the volume of the container.

    Volume of container=100 cm2×20 cm\text{Volume of container} = 100 \text{ cm}^2 \times 20 \text{ cm} Volume of container=2000 cm3\text{Volume of container} = \boxed{2000 \text{ cm}^3}

Part 6.3

1047.20 cm31047.20 \text{ cm}^3

Calculate the volume of the two spheres.

The radius of each sphere is half of its diameter.

Radius of sphere, r=10 cm2=5 cm\text{Radius of sphere, } r = \frac{10 \text{ cm}}{2} = 5 \text{ cm}

The formula for the volume of a single sphere is V=43πr3V = \frac{4}{3} \pi r^3.

  1. Calculate the volume of one sphere.

    Vone sphere=43π(5 cm)3V_{\text{one sphere}} = \frac{4}{3} \pi (5 \text{ cm})^3 Vone sphere=43π(125 cm3)V_{\text{one sphere}} = \frac{4}{3} \pi (125 \text{ cm}^3) Vone sphere=5003π cm3V_{\text{one sphere}} = \frac{500}{3} \pi \text{ cm}^3

  2. Calculate the volume of the two spheres.

    Vtwo spheres=2×Vone sphereV_{\text{two spheres}} = 2 \times V_{\text{one sphere}} Vtwo spheres=2×5003π cm3V_{\text{two spheres}} = 2 \times \frac{500}{3} \pi \text{ cm}^3 Vtwo spheres=10003π cm3V_{\text{two spheres}} = \frac{1000}{3} \pi \text{ cm}^3 Vtwo spheres≈1047.19755 cm3V_{\text{two spheres}} \approx 1047.19755 \text{ cm}^3 Vtwo spheres≈1047.20 cm3V_{\text{two spheres}} \approx \boxed{1047.20 \text{ cm}^3}

Part 6.4

952.80 mL952.80 \text{ mL}

Hence, or otherwise calculate the volume of the empty space in between the spheres inside the container in millilitres.

The volume of the empty space is the volume of the container minus the volume of the two spheres.
Recall that 1 cm3=1 mL1 \text{ cm}^3 = 1 \text{ mL}.

  1. Calculate the volume of the empty space in cm3\text{cm}^3.

    Vempty space=Vcontainer−Vtwo spheresV_{\text{empty space}} = V_{\text{container}} - V_{\text{two spheres}} Vempty space=2000 cm3−10003π cm3V_{\text{empty space}} = 2000 \text{ cm}^3 - \frac{1000}{3} \pi \text{ cm}^3 Vempty space≈2000−1047.19755 cm3V_{\text{empty space}} \approx 2000 - 1047.19755 \text{ cm}^3 Vempty space≈952.80245 cm3V_{\text{empty space}} \approx 952.80245 \text{ cm}^3

  2. Convert the volume to millilitres.

    Vempty space≈952.80 mLV_{\text{empty space}} \approx 952.80 \text{ mL} Vempty space=952.80 mLV_{\text{empty space}} = \boxed{952.80 \text{ mL}}
Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QFind the domain and range of the following functions: 1. 2/sqrt(x³), (x²+1)/(x³+2), 1/cbrt(x)QCounting in groups of 7's, 14's, 30s for everyday use. Study the examples below carefully, and…QThe dlce between the highest & lowest temperatures in addyisQ(7,−3),(5,10),(15,7) and (3,5) taken in order are the corners of a parallelogramQWhat is the equation of a circle with radius 5 and center (−3,2)?
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp