Question

The diameter of the lower upper ends of the bucket in the form of a frustum of a cone are 10cm and 30 cm respectively. If its height is 24cm, find: the areaof the metal sheet used ti make the bucket.

Answer 1

GIVEN :

diameter of upper end of bucket =30cm

radius of the upper end of the frustum of cone( r1) = D/2 = 30/2 => 15cm

d iameter of lower end of bucket = 10 cm

radius of the lower end of the frustum of cone( r2) = D/2=> 10/2 => 5 cm

H of the frustum of Cone = 24 cm

height of bucket ( L)= √(h² + (r1- r2)²

L =√24² + (15 - 5)² = √576 + 10²

L =√(576+(100)= √676 = 26cm

L = 26 cm

area of metal sheet require to make it = π(r1 + r2)L + πr1²

= 3.14(15 + 5) × 26 + π(5)²

= 3.14 × 20 × 26 + 25 × 3.14

= 3.14 (520+ 25)

= 545 × 3.14

= 1711.3 cm²

The Area of metal sheet used to make the bucket is 1711.3 cm².

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@GauravSaxena01

Answer 2

Answer:

Question:-

the length of a rectangle is 8m more than its breadth if its perimeter is 128m, find its length , breadth and Area

Answer:-

The length of Rectangle is 36 m

The breadth of rectangle is 28 m

The area of Given rectangle is 1008 m².

To find:-

Length and breadth of rectangle

Area of rectangle

Solution:-

Let the breadth be x

Length = 8 + x

Perimeter = 128 m

$\boxed{ \large{ \mathfrak{perimeter = 2(l + b)}}}$

According to question,

$\large{ \tt: \implies \: \: \: \: \: 2(8 + x + x) = 128}$

$\begin{gathered} \large{ \tt: \implies \: \: \: \: \: 8 + 2x = \frac{128}{2} } \\ \end{gathered}:$

$\large{ \tt: \implies \: \: \: \: \: 8 + 2x = 64}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 64 - 8}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 56}$

$\large{ \tt: \implies \: \: \: \: \: x = 28}$

The breadth of rectangle is 28 m

Length = 8 + x = 28 + 8 = 36 m

$\large{ \boxed{ \mathfrak{area = l \times b}}}$

$\large{ \tt: \implies \: \: \: \: \: area = 28\times 36}$

$\large{ \tt: \implies \: \: \: \: \: area = 1008 \: {m}^{2} }$

The area of Given rectangle is 1008 m².Question:-

the length of a rectangle is 8m more than its breadth if its perimeter is 128m, find its length , breadth and Area

Answer:-

The length of Rectangle is 36 m

The breadth of rectangle is 28 m

The area of Given rectangle is 1008 m².

To find:-

Length and breadth of rectangle

Area of rectangle

Solution:-

Let the breadth be x

Length = 8 + x

Perimeter = 128 m

$\boxed{ \large{ \mathfrak{perimeter = 2(l + b)}}}$

According to question,

$\large{ \tt: \implies \: \: \: \: \: 2(8 + x + x) = 128}$

$\begin{gathered} \large{ \tt: \implies \: \: \: \: \: 8 + 2x = \frac{128}{2} } \\ \end{gathered}:$

$\large{ \tt: \implies \: \: \: \: \: 8 + 2x = 64}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 64 - 8}$

$\large{ \tt: \implies \: \: \: \: \: 2x = 56}$

$\large{ \tt: \implies \: \: \: \: \: x = 28}$

The breadth of rectangle is 28 m

Length = 8 + x = 28 + 8 = 36 m

$\large{ \boxed{ \mathfrak{area = l \times b}}}$

$\large{ \tt: \implies \: \: \: \: \: area = 28\times 36}$

$\large{ \tt: \implies \: \: \: \: \: area = 1008 \: {m}^{2} }$

The area of Given rectangle is 1008 m².