The diagram shows the solid glass case for a clock. The case is a cuboid with a cylinder

Mathematics

1 answer:

Karolina [17]3 years ago

5 0

Answer:

241.5cm³

Step-by-step explanation:

Volume of the glass = Volume of the cuboid - Volume of the cylinder

Volume of the cuboid = Length * width * height

Volume of the cuboid = 8cm * 4cm * 10cm

Volume of the cuboid = 320cm³

Volume of the cylinder = πr²h

Radius r = 5/2 = 2.5cm

height = 4cm

Volume of the cylinder = 3.14(2.5)²*4

Volume of the cylinder = 78.5cm^3

Volume of the glass = 320 - 78.5

Volume of the glass = 241.5cm³

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3 years ago

Find each absolute value | 4+2i | | 5-i | | -3i |

galina1969 [7]

How to get answer for number 1: | 4+2i |

$\left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2}\\\mathrm{With\:}a=4,\:b=2\\=\sqrt{4^2+2^2}\\Refine\\=\sqrt{20}\\\sqrt{20}=2\sqrt{5}\\=2\sqrt{5}$

How to get answer for number 2: | 5-i |

$\left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2}\\\mathrm{With\:}a=5,\:b=-1\\=\sqrt{5^2+\left(-1\right)^2}\\=\sqrt{26}$

Number 3 how to get answer: | -3i |

$\left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2}\\\mathrm{With\:}a=0,\:b=-3\\=\sqrt{0^2+\left(-3\right)^2}\\Refine\\=\sqrt{9}\\\sqrt{9}\\\mathrm{Factor\:the\:number:\:}\:9=3^2\\=\sqrt{3^2}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a\\\sqrt{3^2}=3\\= 3$