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Question

5)A city sewer pipe has a diameter of 5 feet and a length of 20 feet. Find the volume of the pipe. 


6)An ice cream cone has a diameter of 2 inches and a height of 4 inches. Find its volume. Round your answer to the nearest tenth. 



7)An oil candle globe made of hand-blown glass has a diameter of 16.8 centimeters. What is the volume of the globe? Round your answer to the nearest hundredth. 


8)If one of the angles in a right triangle measures 42 degrees, what are the measures of the other two angles?


9)Find the third side of the right triangle. 
*notes: side a=15cm, side b=36cm 

Answer 1

5).

Diameter of a pipe (d) = 2r = 5 ft ⇒ r = 5/2 ft.

Length (h) = 20 ft.

Volume of the pipe (V) = πr²h.

Substitute the values of r = 5/2, h = 20, and π = 3.14 in V = πr²h.

V = 3.14 * (5/2)² * 20

= 392.5 ft³ .

Volume of the pipe is 392.5 ft³

6).

Diameter of a ice cream cone (d) = 2r = 2 in ⇒ r = 2/2  = 1 in.

Height (h) = 4 in.

Volume of a cone (V) = 1/3(πr²h).

Substitute the values of r = 1, h = 4, and π = 3.14 in V = 1/3(πr²h).

V = 1/3(3.14 *1² * 4)

= 12.56/3

= 4.18.

Volume of the ice cream cone is 4.18 in³ .

Answer 2

7).

Diamerer of an oil candle globe (d) = 2r = 16.8 cm ⇒ r = 16.8/2 = 8.4 cm.

Volume of the globe (V) = 4/3(πr³).

Substitute the values of r = 8.4 and π = 3.14 in V = 4/3(πr³).

V = 4/3(3.14 * 8.4³)

= 2481.45 cm³ .

Volume of the globe is 2481.45 cm³.

8).

Note :

A right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

From the given data,

One of the angles in a  right triangle is 42⁰

Since it is a right triangle, the one angle should be 90⁰

^{Sum of three angles in a triangle is 1800}

^{42 + 90 + x = 180}

^{132 + x = 180}

^{x = 180 - 132 = 48.}

^{Therefore, the other two angles are 480  and 900.}

Answer 3

9).

Pythagorean theorem :

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

This can be stated in equation form as

where c is the length of the hypotenuse, and a and b are the lengths of the remaining two sides.

Given : a = 15 cm, b = 36 cm.

To find c, substitute the values of a = 15 and b = 36 in  c^2 = a^2 + b^2.

c^2 = 15^2 + 36^2

= 225 + 1296

= 1521

c = sqrt (1521) = 39.

Therefore, the third side of the right triangle is 39 cm.