Question

Urgent Help needed !!
(Q1) Find the slanght height of cone whose CSA is 200 cm and Radius is 14 cm.
Q2) Find the perimeter of rectangle whose ratio of length:Breadth is 9:5 and It's perimeter = 140 m.
Q3) Find the Dimensions of cuboid whose Length, Breadth, Height is 3:5:2 and its volume is 500 m.
Q4) What is the area of a rhombus in which its diagonals are 24 cm and 18 cm.

Answer 1

Answer (1)

Given :-

• CSA of cone = 200 cm
• Radius = 14 cm

To Find :-

Slanght height of cone

Solution :-

Concept :- Here, is the concept of a cone whose CSA is 200 cm and it's radius is 14 cm and we have to find its slanght height.

Calculations :-

$\huge \tt \: CSA = \pi \: rl$

Here,

R = Radius

L = Slanght height

π = 22/7

Let the slanght height be l

$\tt \implies \: 200 = \dfrac{22}{7} \times 14 \times l$

$\tt \implies \: 200 = \cancel \dfrac{22}{ 7} \times \cancel {14} \: \times l$

$\tt \implies200 = 22 \times 2 \times l$

$\tt \implies \: 200 = 44l$

$\tt \implies \: l = \dfrac{200}{44}$

$\tt \implies \: l = \cancel \dfrac{200}{44}$

$\tt \implies \: l = 4.545$

Hence :-

The slanght height of cone is 4.545 cm (approx).

Answer (2)

Given :-

• Ratio of length and breadth = 9:5
• Perimeter = 140

To Find :-

Dimensions

Solution :-

Concept :-

Here the perimeter of rectangle is 140 cm and the length and breadth is in ratio 9:5

Calculations :-

Let the sides be x

$\tt \implies \: perimeter \: = 2(l + b)$

$\tt \implies \: 140 = 2(9x + 5x)$

$\tt \implies \: 140 = 18x + 10x$

$\tt \implies \: 140 = 28x$

$\tt \implies \: x = \dfrac{140}{28}$

$\tt \implies \: x = 5$

Now,

Let's find dimensions

$\tt \implies \: length \: = 9x = 9(5) = 45$

$\tt \implies \: breadth \: = 5x = 5(5) = 25$

Answer (3)

Question :-

Find the Dimensions of cuboid whose Length, Breadth, Height is 3:5:2 and its volume is 240 m.

Given :-

Length,Breadth and Height are in ratio 3:5:2

To Find :-

Dimensions

Solution :-

Let's sides be x

As we know that

Volume = l × b × h

240 = 3x × 5x × 2x

240 = 30x³

x³ = 240/30

x³ = 8

x = 2

Length of the given cube =5x=5×2=10cm

Breadth of the given cube =3x=3×2=6cm

Height of the given cube = 2x=2×2 =4cm

Answer (4) :-

Given :-

• Diagonal of rhombus = 24 and 18

To Find :-

Area of rhombus

Solution :-

As we know that

$\huge \bf \: Area \: = \frac{1}{2} \times d1 \times d2$

Area = ½ × 24 × 18

Area = 1 × 12 × 18

Area = 12 × 18

Area = 216 cm