﻿ The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm3. Find its radius. from Mathematics Surface Areas and Volumes Class 10 Uttarakhand Board
The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm3. Find its radius.

Let radius (r) = 5x and height (h) = 7x.
Now. Volume = 550 x = 1
∴ The required radius = 5x = 5 x 1 = 5cm.

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A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 20 cm and radius of the base is 3.5 cm, find the total surface area of the article. Let r cm be the radius, h cm be the height of the cylinder then
r = 3.5 cm
and    h = 20 cm.
Let r1 be the radius of the hemisphere, then
r1 = 3.5 cm
Now,
Total surface area of the area of the article
= curved surface area of the cylinder
+ 2 (curved surface area of hemisphere)
= 2πrh + 2 (2 πr12)
= 2 πrh + 4 πr2    [∵ r = r1]
= 2 π r(h + 2r) 1148 Views

A toy is in the form of a cone mounted on a hemisphere of common base radius 7cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Let r cm be the radius and h cm the height of the cone, then r = 7 cm, and h = 24 cm. Let l cm be the slant height of am cone, then  Let r1 cm be the radius of hemisphere then
r1 = 7 cm
Now, Total surface area of toy
= C.S.A of cone + C.S.A. of hemisphere Tips: - 384 Views

The decorative block shown in fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. Let the side (edge) of the cube be a cm, then a
= 5 cm.
Let radius of the hemisphere be r, then
r = 2.1 cm
Now,
The total surface area of the block
= T.S.A of cube - base area of hemisphere + C.S.A of hemisphere
= 6 (side)2 – r2 + 2r 2
= 150 – r2 + 2 r2
= 150 + 2 Tips: - 673 Views

The interior of building is in the form of a right circular cylinder of radius 7 m and height 6 m, surmounted by a right circular cone of same radius and of vertical angle 60°. Find the cost of painting the building from inside at the rate of Rs. 30/m2

We have, r1 = Radius of the base of the cylinder = 7m
r2 = Radius of the base of the cone = 7 m
h1 = Height of the cylinder = 6m In right triangle EOC, we have Thus, slant height (CE) = 14 m
Now,Surface area of building = Curved surface area of cylinder + curved surface area of cone Cost of painting the building from inside at the rate of Rs. 30/m2
= Rs. (572 x 30) = Rs. 17160.

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A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 100 cm and the diameter of the hemispherical ends is 28 cm, find the cost of polishing the surface of the solid at the rate of 5 paise per sq. cm.

We have,
r = radius of the cylinder
= radius of hemispherical ends = 14 cm
h = height of cylinder = 72 cm
∴ Total surface area = curved surface area of the cylinder + surface areas of hemispherical ends
= (2 rh +2 x 2 r2) cm2
= 2 r (h + 2r) cm2  Now, cost of polishing the surface of the solid at the rate of 5 paise per sq. m 1223 Views