Question

Calculate:

a) Length of AB,correct to 2 decimal place.
b)Length of CE
c) Size of angle CED
d) Size of angle AED

HELP!!
LOTS OF POINTS?!​

Answer 1

Explanation:

✬ Radius = 2.5 cm ✬

Explanation:

Given:

Radius of spherical ball is 3 cm.

Radii of new spherical balls are 1.5 cm and 2 cm.

To Find:

Radius of third spherical ball ?

Solution : Let the radius of third spherical ball be x cm.

If something is melted and recasted into another thing then their volumes will be equal. In short

Volume of 1st thing = Volume of second one.

➯ Let's see here

Volume of big spherical ball will be equal to the sum of volumes of that three small spherical balls.

As we know that

★ Volume of Sphere = 4/3πr³ ★

[ Taking big spherical ball ]

Radius = 3 cm

⟹ Volume = 4/3 × π × (3)³

⟹ 4π/3 × 27

Volume we got = 4π/3 × 27 cm³

[ Taking 3 small spherical balls ]

Radius of first ball (r¹) = 1.5 cm

For second (R) = 2 cm

For third (x) = x cm

Volume = 4/3 × π( sum cubes of radii)

⟹ Volume = 4/3 × π(1.5³ + 2³ + r³)

⟹ 4π/3 (3.375 + 8 + x³)

⟹ 4π/3 ( 11.375 + x³)

Volume we got = 4π/3 (11.375 + x³) cm³

A/q

First volume = Second volume

➮ 4π/3 × 27 = 4π/3 (11.375 + x³)

➮ 27 = 11.375 + x³

➮ 27 – 11.375 = x³

➮ 15.625 = x³

➮ 15625/1000 = x³

➮ 3125/200 = 625/40 = 125/8 = x³

➮ ³√125/8 = x³

➮ 5/2 = x²

➮ 2.5 cm = x

Hence, the measure of radius of third spherical ball is 2.5 cm.

Answer 2

A)The length of AB = 49.12 cm

B) The length of EC = 24 cm

C) The measure of angle CED = 16.26°

D) The measure of angle ∠AED = 106.26°

Explanation:

Given as :

The figure shown is of two triangle

A) In Δ BAE

cos angle =
`(\textrm base)/(\textrm hypotenuse)`

i.e cos 12.2° =
`(AE)/(AB)`

Or, 0.977 =
`(AE)/(AB)`

∴ AB =
`(48)/(.977)`

i.e AB = 49.12 cm

So, The length of AB = 49.12 cm

B) In ΔDCE

As , ∠C = 90°

Pythagoras theorem

ED² = CD² + EC²

Or, EC² = ED² - CD²

Or, EC² = 25² - 7²

Or, EC² = 625 - 49

Or, EC² = 576

Or, EC =
`√(576)`

i.e EC = 24

So, The length of EC = 24 cm

C) In ΔCED

Sin angle =
`(perpendicular)/(hypotenuse)`

Or, sin ∠E =
`(DC)/(DE)`

Or, sin ∠E =
`(7)/(25)`

sin ∠E = 0.28

∴∠ E =
`Sin^(-1)`.28

i.e ∠E = 16.26°

So, The measure of angle CED = 16.26°

D) In ΔAED

∠AED = ∠AEC + ∠ CED

So, ∠AED = 90° + 16.26°

Or, ∠AED = 106.26°

So, The measure of angle ∠AED = 106.26°

Answer