Question

Can you help me find the volume base area latera area and total area please to this problem

Answer 1

BA = 25π,

LA = 25√2π,

TA = 25π + 25√2π,

V = 41 and 2 / 3π

Explanation:

We need to determine the height here, as it is not given, and is quite important to us. The height is a perpendicular line segment to the radius, hence forming a 45 - 45 - 90 degree triangle as you can see. Therefore, by " Converse to Base Angles Theorem " the height should be equal in length to the radius,

( Height = 5 inches = Radius

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Now knowing the height, let's begin by calculating the base area. By it's name, we have to find the area of the base. As it is a circle, let us apply the formula " πr^2 "

`\pi r^2\\= \pi ( 5 )^2\\= 25\pi` - Base Area = 25π

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The lateral area is simply the surface area excluding the base area, the surface area having a formula of " πr^2 + πrl. " Thus, the lateral area can be calculated through the formula " πrl, " but as we are not given the slant height ( l ) we have to use another formula,
`l= √(r^2+h^2)` -

`\pi r( √(r^2+h^2) )\\= \pi( 5 )( √(5^2 + 5^2) )\\= 25√(2) \pi`- Lateral Area = 25√2π

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And the surface area is the base area + lateral area -

`25\pi + 25√(2) \pi` - Surface Area

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The volume of a cone is 1 / 3rd that of a cylinder, with a simple formula of Base * height. Therefore, we can conclude the following -

`1 / 3( 25\pi )( 5 )\\= 25 / 3( 5 )( \pi )\\= 41 (2)/(3)\pi`- Volume = 41 and 2 / 3π