Question

solve the rocket one

Answer 1

Hii friend,

Total height of the rocket = 26 cm

Heigh of the conical part of the rocket (h)= 6 cm

Diameter of the conical part of the rocket = 5 cm.

Radius(R) = D/2 = 5/2 cm

Slant Height (L) = ✓(r)² + (h)² = ✓(5/2)² + (6)² = ✓25/4 + 36 cm = ✓169/4) = 13/2 cm

Diameter of the cylindrical part = 3 cm

Radius of the cylindrical part (r)= D/2 = 3/2 cm

HEIGHT of the cylindrical part of the rocket (H) = Total heigh of the rocket - Height of the conical part of the rocket = 26-6 = 20 cm.

Area of the conical part which is coloured by Green color = CSA of the conical part + Base of the cone - base area of the cylinder.

=> πrl + πr² - πR² = π(rL+r²-R²)

=> [ 3.14 × (5/2 × 13/2 + 5/2 - 3/2 × 3/2)] cm².

=> [ 3.14 × (65/4 + 25/4 -9/4)] cm²

=> [ 3.14 × (65+25-9/4)]

=> (3.14 × 81/4) => (3.14 × 20.25) cm²

=> 63.585 cm².

Area to be painted with red color = CSA of the cylindrical part + Base area of the bottom of the cylinder

=> 2πRH + πR² => πR(2H+R)

=> [ 3.14 × 3/2 ( 2 × 20 + 3/2)] cm²

=> (3.14 × 3/2 × 83/2) cm²

=> (781.86/4) => 195.465 cm².

VOLUME OF THE ROCKET = VOLUME OF CONE + VOLUME OF CYLINDER

=> 1/3πr²h + πR²H

=> π(1/3r²h + R²H)

=> 3.14× (1/3 × 5/2 × 5/2 × 6 + 3/2 × 3/2 × 20)

=> 3.14 × (150/12 + 180/4)

=> 3.14 × (150+540/12)

=> 3.14 × 690/12

=> 2166.6/12

=> 180.55 cm³.

HOPE IT WILL HELP YOU...... :-)

Answer 2

Total height of rocket = 26 cm

height of cone = h = 6 cm

then,
height of cylinder = h¹
= height of rocket - height of cone
= 26 cm - 6 cm
= 20 cm

radius of cone = r1 = 5/2 cm = 2.5 cm
radius of cylinder = r = 3/2 cm = 1.5 cm

1) volume of rocket toy

= volume of cylinder + volume of cone

= πr²h¹ + 1/3 πr1²h

= π(r²h¹+1/3 r1²h)

= π((1.5)²(20) + 1/3(2.5)²(6)

= 3.14(45 + 12.5)

= 3.14(57.5)

= 180.55 cm³

// first find the slant height of cone //
applying Pythagoras thereom
l² = r1² + h²
l² = (2.5)²+(6)²
l² = 42.25
l = √42.25
l = 6.5 cm

2) area of the rocket

= surface area of cylinder + surface area of cone

= 2πrh + πr1l

= π(2rh + r1l)

= π(2×1.5×20 + 2.5×6.5)

= 3.14(60 + 16.25)

= 3.14(76.25)

= 239.425

≈ 239.43 cm²

we also paint the base of cone instead of cylinder upper base,
so area of remain place

= area of circle of the cone - area of the circle of cylinder upper base

= πr1² - πr²

= π(r1² - r²)

= π((2.5)²-(1.5)²

= π(4)

= 3.14(4)

= 12.56 cm²

area of the surface which we painted is

= 239.43 + 12 .56

= 251.99 cm²