Multiple choice A firework rocket consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. The diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in, while the height of the cone is 3 in. Calculate the surface area of the rocket. Leave your answer in terms of π. A.184π sq.in. B.76π sq.in. C.168π sq.in. D.88π sq.in.
Answers
Multiple choice A firework rocket consists of a cone stacked on top of a cylinder, where the radii of the cone and the cylinder are equal. The diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in, while the height of the cone is 3 in. Calculate the surface area of the rocket. Leave your answer in terms of π. A.184π sq.in. B.76π sq.in. C.168π sq.in. D.88π sq.in.
Step-by-step explanation:
The correct answer is (B) 76π sq.in.
Step-by-step explanation:
because the base of the cone and one circular face of the cylinder is not visible,
(2*π*4*5) + (π * 4²)
40π + 16π
= 56π
Lateral Area of a Cone =π rl
Base radius, r= 8/2 =4 Inches
Perpendicular Height of the Cone = 3 Inches
Using Pythagoras theorem:
Hypotenuse =\sqrt{opposite^2+adjacent^2} \\=\sqrt{3^2+4^2} \\=\sqrt{25}\\ =5 in.
√3² + 4²
=√25
=5in
Slant Height of the Cone, l (Hypotenuse) = 5 Inches
∴: Lateral Area of a Cone = π * 4 *5
=20sqinch
∴, Surface area of the rocket
56π + 20π
=76π
The surface area of the rocket=Base Area of the Cylinder+Lateral area of the Cylinder+Lateral Area of the Cone+
Lateral Area of a Cone
Base radius, r= 8/2 =4 Inches
Perpendicular Height of the Cone = 3 Inches
Using Pythagoras theorem:
Answer:
76π sq. in.
Step-by-step explanation:
Hope this helps :)