10. Find the surface area of the triangular prism. The

Mathematics

1 answer:

worty [1.4K]3 years ago

8 0

Answer:

Step-by-step explanation:

The surface area can be found through the formula

SA=2A+(a+b+c)h

in this case, A is the area of the base, a and b are the legs, c is the base of the triangle, and h is the height. By substituting the values 25 and 25 for the legs and 14 for the base and 48 for the height, you will get 3408 sq cm.

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A cylinder has a volume of 105 cubic centimeter what is the volume of a cone with the same base and height?

pychu [463]

Answer:

Step-by-step explanation:

The formula of a volume of a cylinder:

$V_1=\pi r^2H$

r - radius

H - height

The formula of a volume of a cone:

$V_2=\dfrac{1}{3}\pi r^2H$

If the cylinder and the cone have the same base (radius) and the same height, then the volume of the cone is three times smaller than the volume of the cylinder.

$V_2=\dfrac{1}{3}\underbrace{\pi r^2H}_{V_1}$

Therefore:

$V_2=\dfrac{1}{3}V_1\toV_2=\dfrac{1}{3}\cdot105\ cm^3=35\ cm^3$

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3 years ago

What is the area of the shaded segment?

Whitepunk [10]

Answer:

$6\pi-9\sqrt{3$

Step-by-step explanation:

The area of a pie-slice shape can be found with the equation $A=\pi nr^2/360$ where n is the angle of the shape and r is the radius of the circle. In this case, n=60 and r=6. Therefore, the total area of the pie-slice is $\pi (60)(6^2)/360=6 \pi$

Next, the triangle that makes up the unshaded part of the segment is an equilateral triangle because the angle is 60. The area of an equilateral triangle is $\sqrt{3}r^2/4$ where r is the length of one of its side (in this case, r=6). Plugging that in, we get an area of $9 \sqrt{3}$