问题1.如果圆锥体的倾斜高度为6 cm,而其底面的半径为21 cm,则求出圆锥体的曲面面积。 2个
解决方案:
According to the question,
Slant height of cone, l = 60 cm and radius of the base of cone, r = 21 cm
Since, curved surface area of cone = πrl = 22/7 x 21 x 60 =3960 cm2
问题2.圆锥的半径为5厘米,垂直高度为12厘米。找到曲面的面积。
解决方案:
According to the question,
radius of cone, r = 5 cm and height of the tent, h = 12 cm
We have to find the CSA of cone = πrl, but we don’t know the slant height l, therefore
l = √r2 + h2 = √(52 + 122) = 13 cm
Now, CSA of cone = 3.14 x 5 x 13 = 204.1 cm2
问题3.圆锥的半径是7 cm,曲面的面积是176 cm 2 。找到倾斜高度。
解决方案:
According to the question,
Radius of cone, r =7 cm and curved surface area = 176 cm2
We know that, curved surface area of cone = πrl
⇒ 176 = 22/7 x 7 x l
⇒ l = 8 cm
问题4.锥体的高度为21厘米。如果倾斜高度为28厘米,请找到底座的面积。
解决方案:
Given: height, h = 21 cm and slant height, l = 28 cm
We know the relation, l2 = r2 + h2
Therefore, r2 = h2 – l2
⇒ r = √(282 – 212)= 7√7 cm.
Now, area of circular base = πr2
= 22/7 x (7√7)2 = 1078 cm2
问题5.找到半径为6厘米,高度为8厘米的右圆锥的总表面积。
解决方案:
Given radius of cone, r = 6 cm and height of cone, h = 8 cm
We know the relation, l2 = r2 + h2
⇒ l = √(62 + 82) = 10 cm
Now, TSA of a cone = πr(l + r)
= 3.14 x 6 x (10 + 6) = 301.44 cm2
问题6.找到一个圆锥形的曲面,该圆锥形的底半径为5.25厘米,倾斜高度为10厘米。
解决方案:
Given:
base radius of cone, r = 5.25 cm and slant height of the cone, l =10 cm
CSA of cone = πrl = 22/7 x 5.25 x 10 = 165 cm2
问题7:如果圆锥体的倾斜高度为21 m,底部直径为24 m,则求出圆锥体的总表面积。
解决方案:
Given: diameter of the cone = 24 m, therefore radius of the cone = 12 m and slant height of the cone, l =21 m
Now, TSA of a cone = πr(l + r)
= 22/7 x 12 x (21 + 12) = 1244.57 m2
问题8.圆锥体的曲面面积为60πcm 2 。如果圆锥体的倾斜高度为8厘米,请找到底座的半径。
解决方案:
Given: CSA = 60π cm2 and slant height, l = 8 cm.
We know that, curved surface area of cone = πrl
⇒ 60π = π x r x 8
⇒ r = 7.5 cm
问题9.圆锥的曲面面积为4070 cm 2 ,直径为70 cm。它的倾斜高度是多少?
解决方案:
Given: CSA = 4070 cm2 and diameter = 70 cm, therefore, radius = 35 cm.
We know that, curved surface area of cone = πrl
⇒ 4070 = 22/7 x 35 x l
⇒ l = 37 cm
问题10.圆锥的半径和倾斜高度之比为4:7。如果其曲面面积为792 cm 2 ,请找到其半径。
解决方案:
Given: r : l = 4 : 7
Let the radius, r = 4a and slant height, l = 7a
We know that, curved surface area of cone = πrl
⇒ 792 = 22/7 x 4a x 7a
⇒ a2 = 792/88 = 9
⇒ a = 3
Hence, radius of the cone = 4 x 3 = 12 cm