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ss7ja [257]
2 years ago
6

Witch of the expressions below could be used to find the amount of space occupied by the cone​

Mathematics
1 answer:
OleMash [197]2 years ago
3 0

Answer:

V = 1/3 * πr²*h

Step-by-step explanation:

That's the formula for volume of a cone

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A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude ​
I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

  • ( a ) = 35 cm

  • ( b ) = 54 cm

  • ( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

  • <u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

\sf{   \pmb { \longrightarrow \:  \sqrt{s(s - a)(s - b)(s - c)} }}

where ( s ) :

\sf \longrightarrow s = \dfrac{a + b + c}{2}

Therefore, for the given triangle first we will calculate ( s )

\begin {aligned}\quad & \quad \longmapsto  \sf  s =  \dfrac{a + b + c}{2}  \\  & \quad \longmapsto  \sf s =  \dfrac{35 + 54 + 61}{2}  \\ & \quad \longmapsto  \sf s =  \dfrac{150}{2}  \\ & \quad \longmapsto  \sf s  = 75cm \end{aligned}

Now, Area of triangle will be:

\begin{aligned}&:\implies \sf\quad \sf \:  A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \:  A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)}   \\&:\implies \sf\quad \sf \:  A = \sqrt{75 \times 40 \times 21 \times 14}  \\ &:\implies \sf\quad \sf \:  A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5}  \\ &:\implies \sf\quad \sf \:  A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5}  \\ &:\implies \sf\quad \sf \:  A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf   A =939.15 {cm}^{2} }} \end{aligned}

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

\begin{aligned}&:\implies \sf\quad \sf \:  Area =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2}  \times b \times h =939.15 \\ &:\implies \sf\quad \sf \:   \dfrac{1}{2} \times 61 \times h  = 939.15 \\&:\implies \sf\quad \sf \:  h =939.15 \times  \dfrac{2}{61}   \\&:\implies \sf\quad \sf \:  h = \dfrac{1818.3}{61}  \\ &:\implies \sf\quad  \boxed{ \pmb{\sf \:  h =30.79 \: (approx)}} \end{aligned}

3 0
2 years ago
Read 2 more answers
Rp+s=t in terms of r, s,and t
expeople1 [14]

Answer:

p=(t-s)/r

Step-by-step explanation:

This is an equation so all we have to do is solve backwards step by step:

rp+s=t

rp+s-s=t-s

rp/r=(t-s)/r

p=(t-s)/r

8 0
3 years ago
I need help with the perimeter
spin [16.1K]

Step-by-step explanation:

1) Perimeter = 2(l + w)

Perimeter = 2(94 + 64)

Perimeter= 2(158) = 361 cm

2) Fabric required = Area

Area = l × b

Area = 94 × 64

Area = 6016 cm²

7 0
3 years ago
Read 2 more answers
All of the expressions that have the same value as LaTeX: 892\div8892 ÷ 8. Group of answer choices LaTeX: 8920\div808920 ÷ 80 La
algol13

Answer:

(a) 8920\div80

(e) 0.892\div0.008

Step-by-step explanation:

Given

892\div8

Required

Select equivalent expression

8920\div80

894\div10

89.2\div0.08

8.92\div0.8

0.892\div0.008

Start  by solving the given expression (using a calculator)

892\div8 = 111.5

Then we solve the given options (using a calculator)

(a) 8920\div80

8920\div80 = 111.5

(b) 894\div10

894\div10 = 89.4

(c) 89.2\div0.08

89.2\div0.08 = 1115

(d) 8.92\div0.8

8.92\div0.8 = 11.15

(e) 0.892\div0.008

0.892\div0.008 = 111.5

The equivalent expressions are (a) and (e)

5 0
2 years ago
Tourists covered 640 km for a 4 hour ride by car and a 7 hour ride by train. What is the speed of the train, if it is 5 km/h gre
gavmur [86]

Answer:

60 km/h

Step-by-step explanation:

Let us use the x to represent the speed of the car since it is the smaller value.

Then, the distance covered by the car is 4x since was going 4 kph.

The distance covered by the train is (x+5) times 7 or 7x+35.

We know that the total distance covered is 640 km.

Using this information, we can set up the equation 4x+7x+35=640.

By subtracting both sides by 35 and combining the x's, we get a new equation of 11x=605.

After this, we divide both sides by 11 and get x=55.

Lastly, we add 5 to 55 since the train is 5 km faster than the car and that x stood for the car.

Train=60 km/h

5 0
3 years ago
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