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Question 1170245: 1.a) Deduce that the total surface area S of a cylinder closed at both ends with height, H and base radius R is given by: S=2πR(R+H) where π is a constant.
b) Find the volume of S given that H =15.0m and R =5.0m (leaving your answer in terms of π)
c) Calculate the amount of water the tank can hold leaving your answer in terms of π.
d) Calculate the height (h) of a cuboid tank of cross-sectional area 25 metre cube which has the same capacity as the cylinder tank in (c) above.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step.
**1.a) Deduce the Total Surface Area of a Closed Cylinder**
* **Area of the Top and Bottom Circles:** Each circle has an area of πR². Since there are two circles (top and bottom), their combined area is 2πR².
* **Lateral Surface Area (Curved Surface):** Imagine unrolling the side of the cylinder. This forms a rectangle with height H and width equal to the circumference of the base (2πR). Therefore, the lateral surface area is 2πRH.
* **Total Surface Area (S):** To find the total surface area, add the areas of the top, bottom, and lateral surfaces:
S = 2πR² + 2πRH
S = 2πR(R + H)
**1.b) Find the Volume of the Cylinder**
* **Volume Formula:** The volume (V) of a cylinder is given by V = πR²H.
* **Given Values:** H = 15.0 m and R = 5.0 m.
* **Calculation:**
V = π(5.0 m)²(15.0 m)
V = π(25 m²)(15.0 m)
V = 375π m³
**1.c) Calculate the Amount of Water the Tank Can Hold**
The amount of water the tank can hold is equal to its volume.
* **Answer:** The tank can hold 375π m³ of water.
**1.d) Calculate the Height of a Cuboid Tank with the Same Capacity**
* **Cuboid Volume Formula:** The volume of a cuboid is given by V = Area of base × height.
* **Given Information:**
* Volume of the cuboid = Volume of the cylinder = 375π m³
* Cross-sectional area (base area) of the cuboid = 25 m²
* **Calculation:**
375π m³ = 25 m² × h
h = (375π m³) / (25 m²)
h = 15π m
**Answers:**
a) S = 2πR(R + H)
b) V = 375π m³
c) 375π m³
d) h = 15π m
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
In your post, in the last question, you write
". . . cross-sectional area 25 metre cube . . . ".
Dear missis or mister writer, the area is NEVER measures in "metre cube ".
The appropriate unit for the area is " square meter ".
As I noticed from your posts, you make this error systematically.
It tells me a lot about mathematical qualification of a person who created this problem.
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