Download App

Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
✓

Answer

Let r = 5x and h = 12x be the base radius and height of the cone and cylinder respectively.
Slant height of the cone
$\text{l}=\sqrt{\text{r}^2+\text{h}^2}$
$=\sqrt{(5\text{x})^2+(12\text{x}^2)^2}$
$=\sqrt{25\text{x}^2+144\text{x}^2}$
$\Rightarrow\text{l}=13\text{x}$
The total surface area of cylinder
$\text{S}_1=2\pi\text{r}(\text{h}+\text{r})$
The total surface area of cone
$\text{s}_2=2\pi\text{r}(\text{l}+\text{r})$
Now,
$\Rightarrow\frac{\text{S}_1}{\text{S}_2}=\frac{2\pi\text{r}(\text{h}+\text{r})}{\pi\text{r}(\text{l}+\text{r})}$
$=\frac{2(\text{h}+\text{r})}{(\text{l}+\text{r})}$
$\Rightarrow\frac{\text{S}_1}{\text{S}_2}=\frac{2(12\text{x}+5\text{x})}{13\text{x}+5\text{x}}$
$\Rightarrow\frac{\text{S}_1}{\text{S}_2}=\frac{2\times17\text{x}}{18\text{x}}$
$\Rightarrow\text{S}_1:\text{S}_2=17:9$
Hence, the required ratio are 17 : 9

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Surface Areas And Volumes→Surface Areas And Volumes — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Find the values of k for which the given quadratic equation has real and distinct roots:
$kx^2 + 6x + 1 = 0$
→
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its
i) Curved surface area
ii) Total surface area
iii) Volume
→
Find the values of k for which the given quadratic equation has real and distinct root:
$x^2 - kx + 9 = 0$
→
Find the sum of the first 15 terms of each of the following sequences having $n^{th}$ term as
$a_n = 3 + 4n$
→
∆ PQR ~ ∆ LTR. In ∆ PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆ PQR and ∆ LTR, such that $\frac{PQ}{LT} = \frac{3}{4}.$
→
Four equal circles, each of radius a, touch each other. Show that the area between them is $\frac{6}{7}\text{a}^2$ $\Big(\text{Take }\pi=\frac{22}{7}\Big).$
→
Which term of the AP $21, 18, 15, ....$ is $-81$?
→
Find the value of k, if the points A(8, 1) B(3, -4) and C(2, k) are collinear.
→
Disha purchased some beauty products and paid GST of ₹ 1500 . She sold all the beauty products to one customer and collected GST of ₹ 1700. Find the CGST and SGST to be paid.
→
Prove : $\frac{1}{1+\sin \theta}+\frac{1}{1-\sin \theta}=2 \sec ^2 \theta$
→