Question

please answer this..................​

Answer 1

$\huge{\boxed{\fcolorbox{cyan}{pink} {Answer}}}$

$\sf{1. \:The \:radius \:of \:a \:cone \:is \:5cm \:and \:height \:is \:12cm. \:it \:slant \:height 13}$

Given ;

$\sf{radius \:(r) = 5cm}$

$\sf{height \:(h) = 12cm}$

To find ;

$\sf{\:Slant \:height \:of \:Cone (l) = ?¿}$

Now ;

If the slant height of a cone is l and it's height and radius are h and r respectively ;

$~~~~~~~~\sf\boxed{l² = r² + h²}$

$\sf{: ⟹ l² = (5)² + (12)²}$

$\sf{: ⟹ l² = 25 + 144}$

$\sf{: ⟹ l² = 169}$

$\sf{: ⟹ l = \sqrt{169}}$

$\sf{: ⟹ l = 13}$

Length ( slant height ) = 13cm

_______________________________________

$\sf{2. \:The \:lateral \:surface \:of \:Cone \:πrl}$

πrl

$~~~~~~~~\sf\boxed{r = radius}$

$~~~~~~~~\sf\boxed{l = slant \:height}$

_______________________________________

$\sf{3. \:Class \:Mark \:is \:equal \:to}$

$~~~~~~~~\sf\boxed{\frac{Actual \:lower \:limit + \:Actual \:higher \:limit}{2}}$

_______________________________________

$\sf{4. \:The \:range \:of \:the \:data 7, 9, 7, 5, 9, 9, 18, 6, 8, 9 is }$

Fîrst let's arrange the number into asevding order

$\sf{ 5 , 6 , 7 , 7 , 8 , 9 , 9 , 9 , 9 , 18}$

$~~~~~~~~\sf\boxed{range = higher \:value - \:lower \:value}$

$\sf{: ⟹ R = 18 - 5}$

$\sf{: ⟹ R = 13}$

Range = 13

_______________________________________

$\sf{5. \:Area \:of \:a \:triangle \:is \:60cm² \:and \:its \:base \:is \:15cm \:its \:altitude \:is}$

Given ;

$\sf{Area \:of \:triangle = 60cm²}$

$\sf{base \:(b) = 15cm}$

To find ;

$\sf{Altitude \:(h) = ?¿}$

Now ;

$~~~~~~~~\sf\boxed{Area \:of \:triangle = \frac{1}{2} × b × h}$

$\sf{: ⟹ 60 = \frac{1}{2} × 15 × h}$

$\sf{: ⟹ 60 × 2 = 15 × h}$

$\sf{: ⟹ 120 = 15 × h}$

$\sf{: ⟹ \frac{120}{15} = h}$

$\sf{: ⟹ \frac{\cancel{120}^{8}}{\cancel{15}_{1}} = h}$

$\sf{: ⟹ 8 = h}$

Altitude (h) = 8cm

_______________________________________

$\sf{6. \:In \:Heron's \:formula \:"S" \:stands \:for}$

$~~~~~~~~\sf\boxed{Semi \:perimeter (s) = \frac{a + b + c}{2}}$

$~~~~~~~~\sf\boxed{Heron's \:formula = \sqrt{s(s - a)(s - b)(s - c)}}$

So here S stand for semi perimeter .

_______________________________________

$\sf{7. \:A \:cyclic \:parallelogram \:is \:always \:a }$

Rectangle .

_______________________________________

$\sf{8. \:Angles \:in \:the \:same \:segment \:are \:----- \:always \:in \:measure.}$

Equal

⇒ angles in the same segment are equal.

⇒ Angles \(a = a\)

_______________________________________

$\sf{9. \:A \:quadrilateral \:having \:only \:one \:pair \:of \:opposite \:sides \:parallel \:is \:a }$

Trapezium

⇒ We know that in square, rectangle and rhombus two pairs of opposite sides are parallel, so answer can not be square, rectangle or rhombus.

⇒ We also know the properties of trapezium in which only one pair of opposite sides are equal.

_______________________________________

$\sf{10. \:Point \:of \:intersection \:between \:x-axis \:and \:y-axis \:is \:known \:as }$

Origin

⇒ x - axis and y- axis intersect at the origin. SO, point of intersection is (0,0)

_______________________________________