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2 years ago

(08.01 MC)

Mathematics

1 answer:

Brilliant_brown [7]2 years ago

3 0

Answer:

d. 72 in³

Step-by-step explanation:

To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:

From the question volume of the cone = 24 cubic inches

volume of a cone = $\frac{1}{3}$ πr²h

and volume of a cylinder = πr²h

This implies

volume of a cone = $\frac{1}{3}$ πr²h

= $\frac{1}{3}$ (volume of a cylinder)

volume of a cone = $\frac{1}{3}$ (volume of a cylinder)

24 = $\frac{1}{3}$ (volume of a cylinder)

multiply both-side of the equation by 3

24×3 = $\frac{1}{3}$ (volume of a cylinder)

72 =volume of a cylinder

Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches

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The triangle has size with the lengths of 3 cm 13 cm and 14 cm Is it a right triangle?

WITCHER [35]

Answer:

No, it is not a right triangle

Step-by-step explanation:

Let H = 14 cm

B = 3 cm

P = 13 cm

According to pythagoras theorem:

H^2 = P^2 + B^2

14^2 = 13^2 + 3^2

196 = 169 + 9

196 is not equal to 178

Hence, it is not a right triangle

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Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro

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${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

★ Perimeter of land = 400 m.

★ One of the diagonal = 160 m.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Area each of them [son and daughter] will get.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Let, ABCD be the rhombus shaped field and each side of the field be $x$

[ All sides of the rhombus are equal, therefore we will let the each side of the field be $x$ ]

Now,

• Perimeter = 400m

$\longrightarrow \tt AB+BC+CD+AD=400m$

$\longrightarrow \tt x + x + x + x=400$

$\longrightarrow \tt 4x=400$

$\longrightarrow \tt \: x = \dfrac{400}{4}$

$\longrightarrow \tt x= \red{100m}$

$\therefore$ Each side of the field = 100m.

Now, we have to find the area each [son and daughter] will get.

So, For $\triangle$ ABD,

Here,

• a = 100 [AB]

• b = 100 [AD]

• c = 160 [BD]

$\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }$

$\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}$

$\longrightarrow \tt S = \cancel{ \dfrac{360}{2}}$

$\longrightarrow \tt S = 180m$

Using herons formula,

$\star \tt Area \: of \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star$

where

• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

Putting the values,

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(80)(80)(20) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180 \times 80 \times 80 \times 20 }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{9 \times 20 \times 20 \times 80 \times 80}$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{ {3}^{2} \times {20}^{2} \times {80}^{2} }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = 3 \times 20 \times 80$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \red{ 4800 \: {m}^{2} }$

Thus, area of $\triangle$ ABD = 4800 m²

As both the triangles have same sides

So,

Area of $\triangle$ BCD = 4800 m²

Therefore, area each of them [son and daughter] will get = 4800 m²

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

${\underline{\rule{290pt}{2pt}}}$

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1 year ago

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1 year ago