If r is the radius of the sphere, then the surface area of the sphere is given by 4 π r$^{2}$
If we change the shape of a three-dimensional object, the volume of the new shape will be same.
Volume of 15 spheres = Volume of a cone
15 x ($\dfrac{4}{3}$) π r$^{3}$= $\dfrac{1}{3} πr$^{2}$h
5×4 π r$^{3}$ = $\dfrac{1}{3} π 1$^{2}$(15)
20r$^{3}$ = 5
r$^{3}$ = $\dfrac{5}{20}$ = $\dfrac{1}{4}$
r = $\dfrac{1}{3}\sqrt{4}$
Curved surface of bucket = π($R_1 + R_2$) x slant height (l)
Curved Surface = ($\dfrac{22}{7}$) x (25 + 8) x 35
CSA = 22 x 33 x 5 = 3630 sq.cm.
Curved surface area of cylinder = 2πrh
The curved surface area of hemisphere = 2πr$^{2}$
Here, we have two hemispheres.
So, total curved surface area = 2πrh + 2(2πr$^{2}$) = 2πrh + 4πr$^{2}$
Total surface area of tank = CSA of cylinder + CSA of hemisphere
= 2πrh + 2πr$^{2}$= 2π r(h + r)
= 2 x $\dfrac{22}{7}$ x 30(145 + 30) cm$^{2}$
=33000 cm$^{2}$
= 3.3 m$^{2}$
Radius of cylinder = r
Height = h > 2r
Since the sphere is enclosed by a cylinder, the radius of the cylinder will be the radius of the sphere.
Therefore, diameter of sphere = 2r cm
The total surface area of a cube having side a = 6a$^{2}$
If two identical faces of side a are joined together, then the total surface area of the cuboid so formed is 10a$^{2}$.
We know that,
The total surface area of cylinder = 2πrh + 2πr$^{2}$
When one cylinder is placed over the other cylinder of same height and radius, then height of the new cylinder will be 2h and radius will be r.
Thus, the total surface area of the shape so formed = 2πr(2h) + 2πr$^{2}$ = 4πrh + 2πr$^{2}$
Volume of cuboidal lead solid = 9 cm × 11 cm × 12 cm
= 1188 cm$^{3}$
Radius of lead shot = $\dfrac{3}{2}$ cm = 1.5 cm
Volume of each shot = ($\dfrac{4}{3}$)πr$^{3}$
= ($\dfrac{4}{3}$) × ($\dfrac{22}{7}$) × 1.5 × 1.5 × 1.5
= 14.143 cm$^{3}$
Number of lead shots can be made = $\dfrac{1188}{14.143}$= 84 (approx.)