Question

Which shape is formed by rotating a right triangle about its height?
A) Cuboid
B) Cone
C) Cylinder
D) Sphere

Answer 1

Hint:
This question is based on the concept of conics.
A cone is a three – dimensional geometric shape that has length, width and height. A cone has a single flat face i.e. base that’s in the shape of a circle. A cone has only one apex or vertex point.
Volume of cone $ = \dfrac{1}{3}\pi {r^2}h$
Surface area of cone $ = \pi r\left( {l + r} \right)$
Slant height of the cone $ = \sqrt {\left( {{r^2} + {h^2}} \right)} $.

Complete step by step solution:
If we rotate a right triangle about its height, a cone is formed.

Note:
Cuboid: A cuboid is a convex polyhedron bounded by six quadrilateral faces; whose polyhedral graph is the same as that of a cube.
Volume of the cuboid $ = \left( {length \times breadth \times height} \right)$
Perimeter of cuboid $ = 4\left( {length + breadth + height} \right)$
Sphere: A sphere is defined as the det of points that are all at the same distance r from a given point in a three – dimensional space. These are also referred to as the radius and center of the sphere.
Volume of the sphere $ = \dfrac{4}{3}\pi {r^3}$
Surface area of a sphere $ = 4\pi {r^2}$
Cylinder: Cylinder is one of the basic shapes, which has two parallel circular bases at a distance (called a height of cylinder). It is a three – dimensional shape having surface area and volume.
Volume of cylinder $ = \pi {r^2}h$
Curved Surface Area (CSA) $ = 2\pi rh$
Total Surface Area (TSA) $ = 2\pi r\left( {h + r} \right)$ .