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3 years ago

A cone has a diameter of 7.5 ft and a height of 4.25 ft. What is the volume of the cone to the nearest tenth? Use 3.14 for π.

Mathematics

1 answer:

leva [86]3 years ago

3 0

Answer:

The volume of a cone is $62.5\ \text{feet}^3$ .

Step-by-step explanation:

We have,

Diameter of a cone is 7.5 ft

Radius of a cone is 3.75 ft

Height of the cone is 4.25 ft

It is required to find the volume of the cone. The formula of the volume of cone is given by :

$V=\dfrac{1}{3}\pi r^2 h\\\\V=\dfrac{1}{3}\times 3.14\times (3.75)^2\times 4.25\\\\V=62.55\ \text{feet}^3$

So, the volume of a cone is $62.5\ \text{feet}^3$ .

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3 years ago

AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A

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Answer:

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Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

$\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}$ .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

$\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}$ ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

$\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}$ .....(3)

The area of triangle APM is 35m².

$\text{Area of }\triangle APM=\frac{x}{4}$

$35=\frac{x}{4}$

$x=140$

Therefore the area of triangle ABC is 140m².

Using equation (2).

$\text{Area of }\triangle APC=\frac{x}{2}$

$\text{Area of }\triangle APC=\frac{140}{2}$

$\text{Area of }\triangle APC=70$

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

$\triangle BPC=\triangle BPM+\triangle PMC$

$70=35+\triangle PMC$

$35=\triangle PMC$

Therefore the area of triangle PMC is 35m².

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