A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by . Use the formulas and to answer parts a through d below.
a. Find the volume V and surface area SA of the original cylinder.

Ask by Gonzalez Pritchard. in the United States

Nov 04,2024

Question

A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by . Use the formulas and to answer parts a through d below.
a. Find the volume V and surface area SA of the original cylinder.

Ask by Gonzalez Pritchard. in the United States

Nov 04,2024

UpStudy AI · Accepted Answer

Given:
- Radius, $$ r = 8 $$ inches
- Height, $$ h = 4 $$ inches

We are asked to find the volume $$ V $$ and surface area $$ SA $$ of the original cylinder using the formulas:
- Volume, $$ V = \pi r^2 h $$
- Surface Area, $$ SA = 2\pi rh + 2\pi r^2 $$

Let's calculate the volume and surface area of the original cylinder using the given formulas.
Calculate the value by following steps:
- step0: Calculate:
  $$\pi 	imes 8^{2}	imes 4$$
- step1: Transform the expression:
  $$\pi 	imes 2^{6}	imes 2^{2}$$
- step2: Multiply the terms:
  $$\pi 	imes 2^{6+2}$$
- step3: Add the numbers:
  $$\pi 	imes 2^{8}$$
- step4: Evaluate the power:
  $$\pi 	imes 256$$
- step5: Multiply:
  $$256\pi $$
Calculate or simplify the expression $$ 2 * \pi * 8 * 4 + 2 * \pi * 8^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\pi 	imes 8	imes 4+2\pi 	imes 8^{2}$$
- step1: Multiply the terms:
  $$64\pi +2\pi 	imes 8^{2}$$
- step2: Multiply:
  $$64\pi +128\pi $$
- step3: Collect like terms:
  $$\left(64+128ight)\pi $$
- step4: Add the numbers:
  $$192\pi $$
The volume $$ V $$ of the original cylinder is $$ 256\pi $$ cubic inches, and the surface area $$ SA $$ is $$ 192\pi $$ square inches.
The volume $$ V $$ of the original cylinder is $$ 256\pi $$ cubic inches, and the surface area $$ SA $$ is $$ 192\pi $$ square inches.

A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by . Use the formulas and to answer parts a through d below.
a. Find the volume V and surface area SA of the original cylinder.

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Latest Geometry Questions

A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by . Use the formulas and to answer parts a through d below. a. Find the volume V and surface area SA of the original cylinder.

Upstudy AI Solution

Answer

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Latest Geometry Questions

A right circular cylinder has a radius of 8 inches and a height of 4 inches. Decrease the height and radius by . Use the formulas and to answer parts a through d below.
a. Find the volume V and surface area SA of the original cylinder.