A cylinder and a cone have equal bases the height of the calender is 3cm and the area of its base is 100cm3.the cone is placed upon the cylinder volume of the solid figure so formed is 500cm 3 find the total height of the figure
Answers
11 cm
Explanation:
Given:
Base of cylinder = Base of cone ---(1)
Height of cylinder = 3 cm
Area of base of cylinder = 100 cm²
To find:
The height of solid figure (See in the attachment)
What we have to do ?
We don't need to find the radius of any figure.
question is typically based on volume. As we know volume = Area of base × height (h) . Base areas are given so don't waste your time on finding radius.
1st We will find the Volume of cylinder.
2nd We will form a equation of volume of cone
3rd Just Simplify the equation and we will get the answer.
Solution:
Volume of cylinder = Area of base × height
= 100 × 3 cm³⟹ 300 cm³
Area of base of cone = 100 cm² [from 1]
let, The height of cone be x cm.
Volume of cone = 1/3 Area of base × height
= (100 × h)/3 cm³ ⟹ 100h/3 cm³
According to question,
Volume of (cylinder + cone) = 500 cm³
or, 300 + 100h/3= 500
or, 100(3+h/3)=500
or, 3 + h/3 = 5
or, h/3 = 5 - 3
or, h/3 = 2
or, h = 2 × 3
or, h = 6 cm
Therefore, The required height of figure
= (5+6) = 11 cm
Answer:
90 cm²
Explanation:
Given:
3 Cubes of volume 27 cm³ are joined end to end.
To find:
Total Surface Area (T.S.A)
Solution:
\because∵ Volume of cube = 27 cm³
\therefore \textsf{Side of cube} = \sqrt[3]{27} \:\:\:\:\textsf{cm}$^{3}$ \implies 3 \:\:\: \text{cm}
So the side of each cube is 3 cm.
\because∵ All the cubes are joined end to end. (See In Attachment)
\therefore∴ Length(l) of new cuboid = (3+3+3)
= 9 cm
Breadth(b) = 3 cm
Height(h) = 3 cm
So, T.S.A = 2(lb+bh+lh)
= 2{(9×3)+(3×3)+(3×3)}
= 2(27 + 9 + 9) cm²
= 2(45) cm²
= 90 cm²
Additional Information:
Cube : Cube is a 3D shape which contains equal length, breadth and height. It have 8 vertex, 6 face and 12 edges.
e.g Cube and Dice etc.
Formula Related to Cube
Diagonal of cube = a√3 unit
T.S.A """"""""" = 6a² unit²
Volume """""""" = a³ unit³
[Where a is length of any equal side]
Cuboid : Cuboid is also a 3D shape which have similar properties like cube. But it's length breadth and height are not equal.
Formula Related to Cuboid.
Volume of Cuboid = l × b × h unit³
T.S.A of Cuboid= 2(lb+bh+lh) unit²
\textsf{Diagonal of Cuboid} = \sqrt{l^2+b^2+h^2} \:\:\:\:\: \text{unit}Diagonal of Cuboid=
l
2
+b
2
+h
2
unit
[Where l , b and h are length, breadth and height of any Cuboid]